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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(B) $λ is same for both, λ_{p} = λ_{e}$

$P = \frac{h}{λ} same for both$

$P = \sqrt{2 m K}$

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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(D) 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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(B) $λ = \frac{h}{P} = \frac{h}{\sqrt{2 m K E}}$

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

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

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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(B) 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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(D) $λ = \frac{h}{p} = \frac{h}{m v} \Rightarrow v = \frac{h}{m λ}$

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

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]

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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]

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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]