Q76 / 90 · JEE Main 2023 (11 Apr Shift 2) · Physics

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

Correct answer
A
$1 : 43$
B
$1 : 30$
C
$1 : 62$
D
$2 : 43$

Solution

The de-Broglie wavelength is given by

$λ = \frac{h}{p} = \frac{h}{\sqrt{2 m K}} (As, p^{2} = 2 m K)$ .

It is given that

$(K)_{e} = (K)_{p}$

Thus, the ratio of the wavelengths of the proton and electron is

$\frac{λ_{p}}{λ_{e}} = \frac{\sqrt{2 K m_{e}}}{\sqrt{2 K m_{p}}} = \sqrt{\frac{m_{e}}{m_{p}}} = \sqrt{\frac{1}{1849}} = \frac{1}{43}$ .

Hence, the correct answer is option: 'A'.

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

Solution

Relevant Questions

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