Dual Nature Of Radiation And Matter | Physics JEE previous year questions with Solutions

Q 1 :

A proton and an electron are associated with same de-Broglie wavelength. The ratio of their kinetic energies is

$(Assume h = 6.63 \times 10^{- 34} Js, m_{e} = 9.0 \times 10^{- 31} kg and m_{p} = 1836 times m_{e})$ [2024]

$1 : \frac{1}{1836}$
$1 : 1836$
$1 : \sqrt{1836}$
$1 : \frac{1}{\sqrt{1836}}$

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(2)

$λ is same for both, λ_{p} = λ_{e}$

$P = \frac{h}{λ} same for both$

$P = \sqrt{2 m K}$

Hence, $K \propto \frac{1}{m} \Rightarrow \frac{K E_{p}}{K E_{e}} = \frac{m_{e}}{m_{p}} = \frac{1}{1836}$

Q 2 :

A proton and an electron have the same de Broglie wavelength. If $K_{p}$ and $K_{e}$ be the kinetic energies of proton and electron respectively, then choose the correct relation [2024]

$K_{p} = K_{e}^{2}$
$K_{p} = K_{e}$
$K_{p} > K_{e}$
$K_{p} < K_{e}$

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(4)

De Broglie wavelength of proton and electron = $λ$

$∵ λ = \frac{h}{p} \Rightarrow p_{proton} = p_{electron}$

$K E = \frac{p^{2}}{2 m} \Rightarrow KE \propto \frac{1}{m}$

$\frac{K E_{e}}{K E_{p}} = \frac{m_{p}}{m_{e}}$

Q 3 :

A proton, an electron and an alpha particle have the same energies. Their de-Broglie wavelengths will be compared as [2024]

$λ_{e} > λ_{α} > λ_{p}$
$λ_{α} < λ_{p} < λ_{e}$
$λ_{p} < λ_{e} < λ_{α}$
$λ_{p} > λ_{e} > λ_{α}$

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(2)

$λ = \frac{h}{P} = \frac{h}{\sqrt{2 m K E}}$

$KE is same for all . \Rightarrow λ \propto \frac{1}{\sqrt{m}}$

$m_{e} < m_{p} < m_{α} or λ_{e} > λ_{p} > λ_{α}$

Q 4 :

The de-Broglie wavelength of an electron is the same as that of a photon. If velocity of electron is 25 % of the velocity of light, then the ratio of K.E. of electron and K.E. of photon will be [2024]

1/1
1/8
8/1
1/4

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(2)

For photon, $E_{p} = \frac{h c}{λ_{p}} \Rightarrow λ_{p} = \frac{h c}{E_{p}}$

For electron, $λ_{e} = \frac{h}{m_{e} v_{e}} = \frac{h v_{e}}{2 K_{e}}$

Given $v_{e} = 0.25 c$

$λ_{e} = \frac{h \times 0.25 c}{2 K_{e}} = \frac{h c}{8 K_{e}}$

Also $\frac{h c}{E_{p}} = \frac{h c}{8 K_{e}} \Rightarrow \frac{K_{e}}{E_{p}} = \frac{1}{8}$

Q 5 :

The de Broglie wavelengths of a proton and an $α$ particle are $λ$ and $2 λ$ respectively. The ratio of the velocities of proton and $α$ particle will be [2024]

1 : 8
1 : 2
4 : 1
8 : 1

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(4)

$λ = \frac{h}{p} = \frac{h}{m v} \Rightarrow v = \frac{h}{m λ}$

$\frac{v_{p}}{v_{α}} = \frac{m_{α}}{m_{p}} \times \frac{λ_{α}}{λ_{p}} = 4 \times 2 = 8$

Q 6 :

An electron in the ground state of the hydrogen atom has the orbital radius of $5.3 \times 10^{- 11} m$ while that for the electron in third excited state is $8.48 \times 10^{- 10} m$ . The ratio of the de-Broglie wavelengths of electron in the ground state to that in excited state is [2025]

4
9
3
16

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(1)

According to de-Broglie hypothesis, $λ = \frac{h}{m v}$

$m v r = \frac{n h}{2 π} \Rightarrow m v = \frac{n h}{2 π r}$

$λ = \frac{2 π r h}{n h} \Rightarrow λ \propto \frac{r}{n}$

$\frac{λ_{1}}{λ_{4}} = \frac{r_{1} n_{4}}{n_{1} r_{4}} = \frac{5.3 \times 10^{- 11} \times 4}{1 \times 84.8 \times 10^{- 11}}$

$\Rightarrow \frac{λ_{1}}{λ_{4}} = \frac{1}{4}$

Note: Most appropriate answer will be option (1).

Q 7 :

A sub-atomic particle of mass $10^{- 30} kg$ is moving with a velocity $2.21 \times 10^{6} m / s$ . Under the matter wave consideration, the particle will behave closely like __________.

( $h = 6.63 \times 10^{- 34} Js$ ) [2025]

Infra-red radiation
X-ray
Gamma rays
Visible radiation

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(2)

$λ = \frac{h}{p} = \frac{6.63 \times 10^{- 34}}{10^{- 30} \times 2.21 \times 10^{6}}$

$= 3 \times 10^{- 10} m = 3 \overset{\circ}{A} \Rightarrow X - ray$

Hence, particle will behave as X-ray.

Q 8 :

An electron of mass 'm' with an initial velocity $\vec{v} = v_{0} \hat{i} (v_{0} > 0)$ enters an electric field $\vec{E} = - E_{0} \hat{k}$ . If the initial de-Broglie wavelength is $λ_{0}$ , then its value after time t would be [2025]

$\frac{λ_{0}}{\sqrt{1 + \frac{e^{2} E_{0}^{2} t^{2}}{m^{2} v_{0}^{2}}}}$
$\frac{λ_{0}}{\sqrt{1 - \frac{e^{2} E_{0}^{2} t^{2}}{m^{2} v_{0}^{2}}}}$
$λ_{0}$
$λ_{0} \sqrt{1 + \frac{e^{2} E_{0}^{2} t^{2}}{m^{2} v_{0}^{2}}}$

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(1)

$\vec{v} = v_{0} \hat{i} - \frac{E_{0} e}{m} t \hat{k}$

$| \vec{v} | = \sqrt{v_{0}^{2} + \frac{E_{0}^{2} e^{2} t^{2}}{m^{2}}}$

$λ_{0} = \frac{h}{m v_{0}}$

$λ' = \frac{h}{m v_{0} \sqrt{1 + \frac{E_{0}^{2} e^{2} t^{2}}{v_{0}^{2} m^{2}}}}$

$λ' = \frac{λ_{0}}{\sqrt{1 + \frac{E_{0}^{2} e^{2} t^{2}}{v_{0}^{2} m^{2}}}}$

Q 9 :

A proton of mass ' $m_{p}$ ' has same energy as that of a photon of wavelength ' $λ$ '. If the proton is moving at non-relativistic speed, then ratio of its de-Broglie wavelength to the wavelength of photon is. [2025]

$\frac{1}{c} \sqrt{\frac{2 E}{m_{p}}}$
$\frac{1}{c} \sqrt{\frac{E}{m_{p}}}$
$\frac{1}{c} \sqrt{\frac{E}{2 m_{p}}}$
$\frac{1}{2 c} \sqrt{\frac{E}{m_{p}}}$

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(3)

E is missing in the question but considering E as energy.

Energy of photon, $E_{photon} = \frac{h c}{λ_{photon}}$

$\Rightarrow$ Wavelength of photon, $λ_{photon} = \frac{h c}{E}$

Energy of proton, $E_{proton} = \frac{1}{2} m_{p} v^{2} = \frac{p^{2}}{2 m_{p}}$

$\Rightarrow$ Linear momentum of proton, $p = \sqrt{2 m_{p} E}$

or de-Broglie wavelength of proton, $λ_{proton} = \frac{h}{p} = \frac{h}{\sqrt{2 m_{p} E}}$

Ratio $\frac{λ_{proton}}{λ_{photon}} = \frac{h}{\sqrt{2 m_{p} E}} \times \frac{E}{h c} = \frac{1}{c} \sqrt{\frac{E}{2 m_{p}}}$

Q 10 :

If $λ$ and K are de-Broglie Wavelength and kinetic energy, respectively, of a particle with constant mass. The correct graphical representation for the particle will be [2025]

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(2)

$λ = \frac{h}{m v} = \frac{h}{\sqrt{2 m K}}$

$λ^{2} = \frac{h^{2}}{2 m} (\frac{1}{k})$

$Y = c x^{2}$

Upward facing parabola passing through origin.

Q 11 :

An electron with mass 'm' with an initial velocity $(t = 0) \vec{v} = v_{0} \hat{i} (v_{0} > 0)$ enters a magnetic field $\vec{B} = B_{0} \hat{j}$ . If the initial de-Broglie wavelength at t = 0 is $λ_{0}$ then its value after time 't' would be: [2025]

$\frac{λ_{0}}{\sqrt{1 - \frac{e^{2} B_{0}^{2} t^{2}}{m^{2}}}}$
$\frac{λ_{0}}{\sqrt{1 + \frac{e^{2} B_{0}^{2} t^{2}}{m^{2}}}}$
$λ_{0} \sqrt{1 + \frac{e^{2} B_{0}^{2} t^{2}}{m^{2}}}$
$λ_{0}$

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(4)

Speed does not change due to magnetic field, that's why $λ_{debroglie}$ remains unchanged.

Q 12 :

A photo-emissive substance is illuminated with a radiation of wavelength $λ_{i}$ so that it releases electrons with de-Broglie wavelength $λ_{e}$ . The longest wavelength of radiation that can emit photoelectron is $λ_{0}$ . Expression for de-Broglie wavelength is given by:

(m : mass of the electron, h : Planck's constant and c : speed of light) [2025]

$λ_{e} = \sqrt{\frac{h}{2 m c (\frac{1}{λ_{i}} - \frac{1}{λ_{0}})}}$
$λ_{e} = \sqrt{\frac{h λ_{0}}{2 m c}}$
$λ_{e} = \frac{h}{\sqrt{2 m c (\frac{1}{λ_{i}} - \frac{1}{λ_{0}})}}$
$λ_{e} = \sqrt{\frac{h λ_{i}}{2 m c}}$

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(1)

$E = ϕ + K E \Rightarrow \frac{h c}{λ_{e}} = ϕ + K E$

$λ_{e} = \frac{h}{\sqrt{2 m K . E}}, E = \frac{h c}{λ_{i}} and ϕ = \frac{h c}{λ_{0}}$

$\frac{h^{2}}{2 m λ_{e}^{2}} = \frac{h c}{λ_{i}} - \frac{h c}{λ_{0}} \Rightarrow λ_{e} = \sqrt{\frac{h}{2 m c (\frac{1}{λ_{i}} - \frac{1}{λ_{0}})}}$

Q 13 :

An electron is released from rest near an infinite non-conducting sheet of uniform charge density ' $- σ$ '. The rate of change of de-Broglie wave length associated with the electron varies inversely as $n^{th}$ power of time. The numerical value of n is ________. [2025]

(2)

Let the momentum of $e^{-}$ at any time t is p and its de-broglie wavelength is $λ$ .

Then, $p = \frac{h}{λ}$

$\frac{d p}{d t} = \frac{- h}{λ^{2}} \frac{d λ}{d t}$

$m a = F = - \frac{h}{λ^{2}} \frac{d λ}{d t}$ [m = mass of $e^{-}$ ]

Where –ve sign represents decrease in $λ$ with time

$a = - \frac{p^{2}}{m h} \frac{d λ}{d t} = - \frac{m v^{2}}{h} \frac{d λ}{d t}$

$\frac{d λ}{d t} = - \frac{a h}{m v^{2}}$ ... (i)

Here, $a = \frac{q E}{m} = \frac{e}{m} \frac{σ}{2 ε_{0}} = \frac{σ e}{2 m ε_{0}}$

and v = u + at

u = 0, v = at

Substituting values of $a$ and $v$ in equation (i)

$\frac{d λ}{d t} = - \frac{2 h ε_{0}}{σ e t^{2}}$

$\Rightarrow \frac{d λ}{d t} \propto \frac{1}{t^{2}} \Rightarrow n = 2$

Q 14 :

An $α$ -particle, a proton and an electron have the same kinetic energy. Which one of the following is correct in case of their de-Broglie wavelength [2023]

$λ_{α} > λ_{p} > λ_{e}$
$λ_{α} < λ_{p} < λ_{e}$
$λ_{α} = λ_{p} = λ_{e}$
$λ_{α} > λ_{p} < λ_{e}$

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(2)

$λ_{D} = \frac{h}{p} = \frac{h}{\sqrt{2 m K}}$

$∴$ $λ \propto \frac{1}{\sqrt{m}}$

$∵$ $m_{α} > m_{p} > m_{e}$

$λ_{e} > λ_{p} > λ_{α}$

Q 15 :

Electron beam used in an electron microscope, when accelerated by a voltage of 20 kV, has a de-Broglie wavelength of $λ_{0}$ . If the voltage is increased to 40 kV, then the de-Broglie wavelength associated with the electron beam would be [2023]

$\frac{λ_{0}}{2}$
$3 λ_{0}$
$\frac{λ_{0}}{\sqrt{2}}$
$9 λ_{0}$

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(3)

$λ = \frac{h}{\sqrt{2 m V q}}$

$\frac{λ}{λ_{0}} = \sqrt{\frac{20}{40}} \Rightarrow λ = \frac{λ_{0}}{\sqrt{2}}$

Q 16 :

The ratio of de-Broglie wavelength of an $α$ -particle and a proton accelerated from rest by the same potential is $\frac{1}{\sqrt{m}}$ , the value of $m$ is [2023]

4
16
8
2

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(3)

$\frac{λ_{α}}{λ_{p}} = \frac{h}{\sqrt{2 m_{α} q_{α} V}} = \frac{h}{\sqrt{2 m_{p} q_{p} V}}$

$\frac{λ_{α}}{λ_{p}} = \sqrt{\frac{1}{8}} \Rightarrow m = 8$

Q 17 :

An electron accelerated through a potential difference $V_{1}$ has a de-Broglie wavelength of $λ$ . When the potential is changed to $V_{2}$ , its de-Broglie wavelength increases by 50%. The value of $(\frac{V_{1}}{V_{2}})$ is equal to [2023]

$3$
$\frac{9}{4}$
$\frac{3}{2}$
$4$

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(2)

$K.E. = \frac{P^{2}}{2 m}, P = \frac{h}{λ}$

$e V_{1} = \frac{{(\frac{h}{λ})}^{2}}{2 m}$

$e V_{2} = \frac{{(\frac{h}{1.5 λ})}^{2}}{2 m}$

$\frac{V_{1}}{V_{2}} = {(1.5)}^{2} = \frac{9}{4}$

Q 18 :

Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R. [2023]

Assertion A: The beam of electrons shows wave nature and exhibit interference and diffraction.

Reason R: Davisson Germer experimentally verified the wave nature of electrons.

In the light of the above statements, choose the most appropriate answer from the options given below:

A is correct but R is not correct
A is not correct but R is correct
Both A and R are correct but R is not the correct explanation of A
Both A and R are correct and R is the correct explanation of A

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(4)

Beam of electrons show wave nature and exhibit interference and diffraction as shown by Davisson Germer experiment.

Q 19 :

A proton moving with one tenth of velocity of light has a certain de Broglie wavelength of $λ$ . An alpha particle having certain kinetic energy has the same de-Broglie wavelength $λ$ . The ratio of kinetic energy of proton and that of alpha particle is [2023]

2 : 1
4 : 1
1 : 2
1 : 4

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(2)

$KE = \frac{p^{2}}{2 m} = \frac{h^{2}}{2 m λ^{2}}$

$\frac{{KE}_{p}}{{KE}_{α}} = \frac{m_{α}}{m_{p}} = 4 : 1$

Q 20 :

The kinetic energy of an electron, $α$ -particle and a proton are given as 4K, 2K and K respectively. The de-Broglie wavelength associated with electron $(λ_{e})$ , $α$ -particle $(λ_{α})$ and the proton $(λ_{p})$ are as follows [2023]

$λ_{α} = λ_{p} > λ_{e}$
$λ_{α} > λ_{p} > λ_{e}$
$λ_{α} < λ_{p} < λ_{e}$
$λ_{α} = λ_{p} < λ_{e}$

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(3)

	Electron	Alpha	Proton
Mass:	$\frac{m}{1840}$	$4 m$	$m$
Charge:	$e$	$2 e$	$e$
Kinetic energy:	$4 K$	$2 K$	$K$
$λ = \frac{h}{\sqrt{2 m K}}$	$\frac{h}{\sqrt{2 \cdot (\frac{m}{1840}) \cdot 4 K}}$	$\frac{h}{\sqrt{2.4 m . 2 K}}$	$\frac{h}{\sqrt{2 m K}}$

$λ_{α} < λ_{p} < λ_{e}$

Q 21 :

Proton (P) and electron (e) will have same de-Broglie wavelength when the ratio of their momentum is (assume, $m_{P} = 1849 m_{e}$ ) [2023]

1 : 43
1 : 1
43 : 1
1 : 1849

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(2)

$De Broglie wavelength is λ = \frac{h}{m v}$

$λ_{p} = λ_{e} \Rightarrow m_{p} v_{p} = m_{e} v_{e} \Rightarrow p_{p} = p_{e}$

Q 22 :

The de Broglie wavelength of a molecule in a gas at room temperature (300 K) is $λ_{1}$ . If the temperature of the gas is increased to 600 K, then the de Broglie wavelength of the same gas molecule becomes [2023]

$\frac{1}{\sqrt{2}} λ_{1}$
$2 λ_{1}$
$\frac{1}{2} λ_{1}$
$\sqrt{2} λ_{1}$

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(1)

$From K.T.G$

$v_{RMS} = \sqrt{\frac{3 k_{B} T}{m}}$

$v_{RMS} \propto \sqrt{T} and \frac{h}{m v_{RMS}} = λ \Rightarrow λ \propto \frac{1}{\sqrt{T}}$

$\frac{λ_{2}}{λ_{1}} = \sqrt{\frac{T_{1}}{T_{2}}} = \sqrt{\frac{300}{600}} = \frac{1}{\sqrt{2}}$

$\Rightarrow λ_{2} = \frac{λ_{1}}{\sqrt{2}}$

Q 23 :

The ratio of the de-Broglie wavelengths of proton and electron having same kinetic energy (Assume $m_{p} = m_{e} \times 1849$ ) [2023]

1 : 43
1 : 30
1 : 62
2 : 43

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(1)

$λ \propto \frac{1}{\sqrt{m}} \Rightarrow \frac{λ_{p}}{λ_{e}} = \sqrt{\frac{m_{e}}{m_{p}}} = 1 : 43$

Q 24 :

A proton and an $α$ -particle are accelerated from rest by 2V and 4V potential, respectively. The ratio of their de-Broglie wavelength is: [2023]

4 : 1
2 : 1
8 : 1
16 : 1

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(1)

$λ = \frac{h}{m v} = \frac{h}{\sqrt{2 m K}} = \frac{h}{\sqrt{2 m q Δ V}}$

$\frac{λ_{α}}{λ_{p}} = \sqrt{\frac{m_{p} V_{p} q_{p}}{m_{α} V_{α} q_{α}}}$

$\Rightarrow \frac{λ_{α}}{λ_{p}} = \sqrt{\frac{1 \times 2 \times 1}{4 \times 4 \times 2}} = \frac{1}{4}$

$\Rightarrow λ_{p} : λ_{α} = 4 : 1$

Q 25 :

The de Broglie wavelength of an electron having kinetic energy E is $λ$ . If the kinetic energy of electron becomes $\frac{E}{4}$ , then its de-Broglie wavelength will be [2023]

$\frac{λ}{\sqrt{2}}$
$\frac{λ}{2}$
$2 λ$
$\sqrt{2} λ$

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(3)

$λ = \frac{h}{\sqrt{2 m E}}$

$λ' = \frac{h}{\sqrt{2 m (\frac{E}{4})}} = \frac{2 h}{\sqrt{2 m E}} = 2 λ$

Q 26 :

The de Broglie wavelength of an oxygen molecule at $27 ° C$ is $x \times 10^{- 12} m$ . The value of $x$ is (take Planck’s constant $= 6.63 \times 10^{- 34} J.s$ , Boltzmann constant $= 1.38 \times 10^{- 23} J/K$ , mass of oxygen molecule $= 5.31 \times 10^{- 26} kg$ ). [2026]

20
30
26
24

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(3)

$λ = \frac{h}{\sqrt{2 m K}} = \frac{h}{\sqrt{2 m (\frac{3}{2} k T)}}$

$λ = \frac{h}{\sqrt{3 m k T}}$

$= \frac{6.63 \times 10^{- 34}}{\sqrt{3 \times 5.31 \times 10^{- 26} \times 1.38 \times 10^{- 23} \times 300}}$

$= 2.58 \times 10^{- 11} = 25.8 \times 10^{- 12}$

$So, x = 26$

Q 27 :

A particle having electric charge $3 \times 10^{- 19} C$ and mass $6 \times 10^{- 27} kg$ is accelerated by applying an electric potential of 1.21 V. Wavelength of the matter wave associated with the particle is $α \times 10^{- 12} m$ . The value of $α$ is_______.

$(Take Planck's constant = 6.6 \times 10^{- 34} J·s)$ [2026]

(10)

$λ = \frac{h}{\sqrt{2 m q V}}$

$λ = \frac{6.6 \times 10^{- 34}}{\sqrt{2 \times 18 \times 10^{- 46} \times 1.21}}$

$λ = 10^{- 11} m = 10 \times 10^{- 12} m$

$α = 10$

Q 28 :

The ratio of de Broglie wavelength of a deuteron with kinetic energy E to that of an alpha particle with kinetic energy 2E is $n : 1$ . The value of n is ____. [2026]

(Assume mass of proton = mass of neutron.)

(2)

$λ = \frac{h}{m v} = \frac{h}{\sqrt{2 m \cdot K E}}$

$\frac{λ_{d}}{λ_{α}} = \sqrt{\frac{m_{α} \cdot K E_{α}}{m_{d} \cdot K E_{d}}} = \sqrt{\frac{4 m \cdot 2 E}{2 m \cdot E}} = 2 : 1$

Topic Question Set

Q 1 :

A proton and an electron are associated with same de-Broglie wavelength. The ratio of their kinetic energies is

$(Assume h = 6.63 \times 10^{- 34} Js, m_{e} = 9.0 \times 10^{- 31} kg and m_{p} = 1836 times m_{e})$ [2024]

Q 2 :

A proton and an electron have the same de Broglie wavelength. If $K_{p}$ and $K_{e}$ be the kinetic energies of proton and electron respectively, then choose the correct relation [2024]

Q 3 :

A proton, an electron and an alpha particle have the same energies. Their de-Broglie wavelengths will be compared as [2024]

Q 4 :

The de-Broglie wavelength of an electron is the same as that of a photon. If velocity of electron is 25 % of the velocity of light, then the ratio of K.E. of electron and K.E. of photon will be [2024]

Q 5 :

The de Broglie wavelengths of a proton and an $α$ particle are $λ$ and $2 λ$ respectively. The ratio of the velocities of proton and $α$ particle will be [2024]

Q 6 :

An electron in the ground state of the hydrogen atom has the orbital radius of $5.3 \times 10^{- 11} m$ while that for the electron in third excited state is $8.48 \times 10^{- 10} m$ . The ratio of the de-Broglie wavelengths of electron in the ground state to that in excited state is [2025]

Q 7 :

A sub-atomic particle of mass $10^{- 30} kg$ is moving with a velocity $2.21 \times 10^{6} m / s$ . Under the matter wave consideration, the particle will behave closely like __________.

( $h = 6.63 \times 10^{- 34} Js$ ) [2025]

Q 8 :

An electron of mass 'm' with an initial velocity $\vec{v} = v_{0} \hat{i} (v_{0} > 0)$ enters an electric field $\vec{E} = - E_{0} \hat{k}$ . If the initial de-Broglie wavelength is $λ_{0}$ , then its value after time t would be [2025]

Q 9 :

A proton of mass ' $m_{p}$ ' has same energy as that of a photon of wavelength ' $λ$ '. If the proton is moving at non-relativistic speed, then ratio of its de-Broglie wavelength to the wavelength of photon is. [2025]

Q 10 :

If $λ$ and K are de-Broglie Wavelength and kinetic energy, respectively, of a particle with constant mass. The correct graphical representation for the particle will be [2025]

Q 11 :

An electron with mass 'm' with an initial velocity $(t = 0) \vec{v} = v_{0} \hat{i} (v_{0} > 0)$ enters a magnetic field $\vec{B} = B_{0} \hat{j}$ . If the initial de-Broglie wavelength at t = 0 is $λ_{0}$ then its value after time 't' would be: [2025]

Q 13 :

An electron is released from rest near an infinite non-conducting sheet of uniform charge density ' $- σ$ '. The rate of change of de-Broglie wave length associated with the electron varies inversely as $n^{th}$ power of time. The numerical value of n is ________. [2025]

Q 14 :

An $α$ -particle, a proton and an electron have the same kinetic energy. Which one of the following is correct in case of their de-Broglie wavelength [2023]

Q 15 :

Electron beam used in an electron microscope, when accelerated by a voltage of 20 kV, has a de-Broglie wavelength of $λ_{0}$ . If the voltage is increased to 40 kV, then the de-Broglie wavelength associated with the electron beam would be [2023]

Q 16 :

The ratio of de-Broglie wavelength of an $α$ -particle and a proton accelerated from rest by the same potential is $\frac{1}{\sqrt{m}}$ , the value of $m$ is [2023]

Q 17 :

An electron accelerated through a potential difference $V_{1}$ has a de-Broglie wavelength of $λ$ . When the potential is changed to $V_{2}$ , its de-Broglie wavelength increases by 50%. The value of $(\frac{V_{1}}{V_{2}})$ is equal to [2023]

Q 19 :

A proton moving with one tenth of velocity of light has a certain de Broglie wavelength of $λ$ . An alpha particle having certain kinetic energy has the same de-Broglie wavelength $λ$ . The ratio of kinetic energy of proton and that of alpha particle is [2023]

Q 20 :

The kinetic energy of an electron, $α$ -particle and a proton are given as 4K, 2K and K respectively. The de-Broglie wavelength associated with electron $(λ_{e})$ , $α$ -particle $(λ_{α})$ and the proton $(λ_{p})$ are as follows [2023]

Q 21 :

Proton (P) and electron (e) will have same de-Broglie wavelength when the ratio of their momentum is (assume, $m_{P} = 1849 m_{e}$ ) [2023]

Q 22 :

The de Broglie wavelength of a molecule in a gas at room temperature (300 K) is $λ_{1}$ . If the temperature of the gas is increased to 600 K, then the de Broglie wavelength of the same gas molecule becomes [2023]

Q 23 :

The ratio of the de-Broglie wavelengths of proton and electron having same kinetic energy (Assume $m_{p} = m_{e} \times 1849$ ) [2023]

Q 24 :

A proton and an $α$ -particle are accelerated from rest by 2V and 4V potential, respectively. The ratio of their de-Broglie wavelength is: [2023]

Q 25 :

The de Broglie wavelength of an electron having kinetic energy E is $λ$ . If the kinetic energy of electron becomes $\frac{E}{4}$ , then its de-Broglie wavelength will be [2023]

Q 26 :

The de Broglie wavelength of an oxygen molecule at $27 ° C$ is $x \times 10^{- 12} m$ . The value of $x$ is (take Planck’s constant $= 6.63 \times 10^{- 34} J.s$ , Boltzmann constant $= 1.38 \times 10^{- 23} J/K$ , mass of oxygen molecule $= 5.31 \times 10^{- 26} kg$ ). [2026]

Q 28 :

The ratio of de Broglie wavelength of a deuteron with kinetic energy E to that of an alpha particle with kinetic energy 2E is $n : 1$ . The value of n is ____. [2026]

(Assume mass of proton = mass of neutron.)

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Topic Question Set

Q 1 : A proton and an electron are associated with same de-Broglie wavelength. The ratio of their kinetic energies is (Assume h=6.63×10-34 Js,me=9.0×10-31 kg and mp=1836 times me) [2024]

Q 2 : A proton and an electron have the same de Broglie wavelength. If Kp and Ke be the kinetic energies of proton and electron respectively, then choose the correct relation [2024]

Q 3 : A proton, an electron and an alpha particle have the same energies. Their de-Broglie wavelengths will be compared as [2024]

Q 4 : The de-Broglie wavelength of an electron is the same as that of a photon. If velocity of electron is 25 % of the velocity of light, then the ratio of K.E. of electron and K.E. of photon will be [2024]

Q 5 : The de Broglie wavelengths of a proton and an α particle are λ and 2λ respectively. The ratio of the velocities of proton and α particle will be [2024]

Q 6 : An electron in the ground state of the hydrogen atom has the orbital radius of 5.3×10–11 m while that for the electron in third excited state is 8.48×10–10 m. The ratio of the de-Broglie wavelengths of electron in the ground state to that in excited state is [2025]

Q 7 : A sub-atomic particle of mass 10–30 kg is moving with a velocity 2.21×106 m/s. Under the matter wave consideration, the particle will behave closely like __________. (h=6.63×10–34 Js) [2025]

Q 8 : An electron of mass 'm' with an initial velocity v→=v0i^(v0>0) enters an electric field E→=–E0k^. If the initial de-Broglie wavelength is λ0, then its value after time t would be [2025]

Q 9 : A proton of mass 'mp' has same energy as that of a photon of wavelength 'λ'. If the proton is moving at non-relativistic speed, then ratio of its de-Broglie wavelength to the wavelength of photon is. [2025]

Q 10 : If λ and K are de-Broglie Wavelength and kinetic energy, respectively, of a particle with constant mass. The correct graphical representation for the particle will be [2025]

Q 11 : An electron with mass 'm' with an initial velocity (t=0)v→=v0i^(v0>0) enters a magnetic field B→=B0j^. If the initial de-Broglie wavelength at t = 0 is λ0 then its value after time 't' would be: [2025]

Q 13 : An electron is released from rest near an infinite non-conducting sheet of uniform charge density '–σ'. The rate of change of de-Broglie wave length associated with the electron varies inversely as nth power of time. The numerical value of n is ________. [2025]

Q 14 : An α-particle, a proton and an electron have the same kinetic energy. Which one of the following is correct in case of their de-Broglie wavelength [2023]

Q 15 : Electron beam used in an electron microscope, when accelerated by a voltage of 20 kV, has a de-Broglie wavelength of λ0. If the voltage is increased to 40 kV, then the de-Broglie wavelength associated with the electron beam would be [2023]

Q 16 : The ratio of de-Broglie wavelength of an α-particle and a proton accelerated from rest by the same potential is 1m, the value of m is [2023]

Q 17 : An electron accelerated through a potential difference V1 has a de-Broglie wavelength of λ. When the potential is changed to V2, its de-Broglie wavelength increases by 50%. The value of (V1V2) is equal to [2023]

Q 19 : A proton moving with one tenth of velocity of light has a certain de Broglie wavelength of λ. An alpha particle having certain kinetic energy has the same de-Broglie wavelength λ. The ratio of kinetic energy of proton and that of alpha particle is [2023]

Q 20 : The kinetic energy of an electron, α-particle and a proton are given as 4K, 2K and K respectively. The de-Broglie wavelength associated with electron (λe), α-particle (λα) and the proton (λp) are as follows [2023]

Q 21 : Proton (P) and electron (e) will have same de-Broglie wavelength when the ratio of their momentum is (assume, mP=1849 me) [2023]

Q 22 : The de Broglie wavelength of a molecule in a gas at room temperature (300 K) is λ1. If the temperature of the gas is increased to 600 K, then the de Broglie wavelength of the same gas molecule becomes [2023]

Q 23 : The ratio of the de-Broglie wavelengths of proton and electron having same kinetic energy (Assume mp=me×1849) [2023]

Q 24 : A proton and an α-particle are accelerated from rest by 2V and 4V potential, respectively. The ratio of their de-Broglie wavelength is: [2023]

Q 25 : The de Broglie wavelength of an electron having kinetic energy E is λ. If the kinetic energy of electron becomes E4, then its de-Broglie wavelength will be [2023]

Q 26 : The de Broglie wavelength of an oxygen molecule at 27°C is x×10-12 m. The value of x is (take Planck’s constant =6.63×10-34 J.s, Boltzmann constant =1.38×10-23 J/K, mass of oxygen molecule =5.31×10-26 kg). [2026]

Q 27 : A particle having electric charge 3×10-19 C and mass 6×10-27 kg is accelerated by applying an electric potential of 1.21 V. Wavelength of the matter wave associated with the particle is α×10-12 m. The value of α is_______. (Take Planck's constant =6.6×10-34 J·s) [2026]

Q 28 : The ratio of de Broglie wavelength of a deuteron with kinetic energy E to that of an alpha particle with kinetic energy 2E is n:1. The value of n is ____. [2026] (Assume mass of proton = mass of neutron.)

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Q 1 :

A proton and an electron are associated with same de-Broglie wavelength. The ratio of their kinetic energies is

$(Assume h = 6.63 \times 10^{- 34} Js, m_{e} = 9.0 \times 10^{- 31} kg and m_{p} = 1836 times m_{e})$ [2024]

Q 2 :

A proton and an electron have the same de Broglie wavelength. If $K_{p}$ and $K_{e}$ be the kinetic energies of proton and electron respectively, then choose the correct relation [2024]

Q 3 :

A proton, an electron and an alpha particle have the same energies. Their de-Broglie wavelengths will be compared as [2024]

Q 4 :

The de-Broglie wavelength of an electron is the same as that of a photon. If velocity of electron is 25 % of the velocity of light, then the ratio of K.E. of electron and K.E. of photon will be [2024]

Q 5 :

The de Broglie wavelengths of a proton and an $α$ particle are $λ$ and $2 λ$ respectively. The ratio of the velocities of proton and $α$ particle will be [2024]

Q 6 :

An electron in the ground state of the hydrogen atom has the orbital radius of $5.3 \times 10^{- 11} m$ while that for the electron in third excited state is $8.48 \times 10^{- 10} m$ . The ratio of the de-Broglie wavelengths of electron in the ground state to that in excited state is [2025]

Q 7 :

A sub-atomic particle of mass $10^{- 30} kg$ is moving with a velocity $2.21 \times 10^{6} m / s$ . Under the matter wave consideration, the particle will behave closely like __________.

( $h = 6.63 \times 10^{- 34} Js$ ) [2025]

Q 8 :

An electron of mass 'm' with an initial velocity $\vec{v} = v_{0} \hat{i} (v_{0} > 0)$ enters an electric field $\vec{E} = - E_{0} \hat{k}$ . If the initial de-Broglie wavelength is $λ_{0}$ , then its value after time t would be [2025]

Q 9 :

A proton of mass ' $m_{p}$ ' has same energy as that of a photon of wavelength ' $λ$ '. If the proton is moving at non-relativistic speed, then ratio of its de-Broglie wavelength to the wavelength of photon is. [2025]

Q 10 :

If $λ$ and K are de-Broglie Wavelength and kinetic energy, respectively, of a particle with constant mass. The correct graphical representation for the particle will be [2025]

Q 11 :

An electron with mass 'm' with an initial velocity $(t = 0) \vec{v} = v_{0} \hat{i} (v_{0} > 0)$ enters a magnetic field $\vec{B} = B_{0} \hat{j}$ . If the initial de-Broglie wavelength at t = 0 is $λ_{0}$ then its value after time 't' would be: [2025]

Q 13 :

An electron is released from rest near an infinite non-conducting sheet of uniform charge density ' $- σ$ '. The rate of change of de-Broglie wave length associated with the electron varies inversely as $n^{th}$ power of time. The numerical value of n is ________. [2025]

Q 14 :

An $α$ -particle, a proton and an electron have the same kinetic energy. Which one of the following is correct in case of their de-Broglie wavelength [2023]

Q 15 :

Electron beam used in an electron microscope, when accelerated by a voltage of 20 kV, has a de-Broglie wavelength of $λ_{0}$ . If the voltage is increased to 40 kV, then the de-Broglie wavelength associated with the electron beam would be [2023]

Q 16 :

The ratio of de-Broglie wavelength of an $α$ -particle and a proton accelerated from rest by the same potential is $\frac{1}{\sqrt{m}}$ , the value of $m$ is [2023]

Q 17 :

An electron accelerated through a potential difference $V_{1}$ has a de-Broglie wavelength of $λ$ . When the potential is changed to $V_{2}$ , its de-Broglie wavelength increases by 50%. The value of $(\frac{V_{1}}{V_{2}})$ is equal to [2023]

Q 19 :

A proton moving with one tenth of velocity of light has a certain de Broglie wavelength of $λ$ . An alpha particle having certain kinetic energy has the same de-Broglie wavelength $λ$ . The ratio of kinetic energy of proton and that of alpha particle is [2023]

Q 20 :

The kinetic energy of an electron, $α$ -particle and a proton are given as 4K, 2K and K respectively. The de-Broglie wavelength associated with electron $(λ_{e})$ , $α$ -particle $(λ_{α})$ and the proton $(λ_{p})$ are as follows [2023]

Q 21 :

Proton (P) and electron (e) will have same de-Broglie wavelength when the ratio of their momentum is (assume, $m_{P} = 1849 m_{e}$ ) [2023]

Q 22 :

The de Broglie wavelength of a molecule in a gas at room temperature (300 K) is $λ_{1}$ . If the temperature of the gas is increased to 600 K, then the de Broglie wavelength of the same gas molecule becomes [2023]

Q 23 :

The ratio of the de-Broglie wavelengths of proton and electron having same kinetic energy (Assume $m_{p} = m_{e} \times 1849$ ) [2023]

Q 24 :

A proton and an $α$ -particle are accelerated from rest by 2V and 4V potential, respectively. The ratio of their de-Broglie wavelength is: [2023]

Q 25 :

The de Broglie wavelength of an electron having kinetic energy E is $λ$ . If the kinetic energy of electron becomes $\frac{E}{4}$ , then its de-Broglie wavelength will be [2023]

Q 26 :

The de Broglie wavelength of an oxygen molecule at $27 ° C$ is $x \times 10^{- 12} m$ . The value of $x$ is (take Planck’s constant $= 6.63 \times 10^{- 34} J.s$ , Boltzmann constant $= 1.38 \times 10^{- 23} J/K$ , mass of oxygen molecule $= 5.31 \times 10^{- 26} kg$ ). [2026]

Q 28 :

The ratio of de Broglie wavelength of a deuteron with kinetic energy E to that of an alpha particle with kinetic energy 2E is $n : 1$ . The value of n is ____. [2026]

(Assume mass of proton = mass of neutron.)