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

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Solution

Q.
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 $1 : \frac{1}{1836}$

2 $1 : 1836$

3 $1 : \sqrt{1836}$

4 $1 : \frac{1}{\sqrt{1836}}$

Ans.
(2)

$λ is same for both, λ_{p} = λ_{e}$

$P = \frac{h}{λ} same for both$

$P = \sqrt{2 m K}$

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

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