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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4

(none)

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

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

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

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

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

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)

$λ = \frac{h}{p} = \frac{6.63 \times 10^{- 34}}{10^{- 30} \times 2.21 \times 10^{- 11}}$

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

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.

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]

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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]

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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]