According to de-Broglie hypothesis if an electron of mass ' m ' is accelerated by potential difference ' V ', the associated wavelength is ' λ '. When a proton of mass ' M ' is accelerated through potential difference 9 V, then the wavelength associated with it is (a) (λ)/(3)√(m/M) (b) 3/2√(m/M) (c) (λ)/(3)√(M/m) (d) (3)/(λ)√(M/m)

Answer: (a). Electron: λ = (h)/(√(2meV)). Proton: λp = (h)/(√(2Me(9V))) = 1/3√(m/M) · (h)/(√(2meV)) λp = (λ)/(3)√(m/M), so the answer is (a).

According to de-Broglie hypothesis if an electron of mass ' m ' is… | MHT CET 2021 (23 Sep, Shift 2)

Q100MHT CET 2021 · 23 SEP · SHIFT 2Medium

Matter Waves: de Broglie Wavelength

According to de-Broglie hypothesis if an electron of mass ' $m$ ' is accelerated by potential difference ' $V$ ', the associated wavelength is ' $\lambda$ '. When a proton of mass ' $M$ ' is accelerated through potential difference $9\text{ V}$ , then the wavelength associated with it is

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Answer: (a)

Electron: $\lambda = \dfrac{h}{\sqrt{2meV}}$ .
Proton: $\lambda_p = \dfrac{h}{\sqrt{2Me(9V)}} = \dfrac{1}{3}\sqrt{\dfrac{m}{M}} \cdot \dfrac{h}{\sqrt{2meV}}$
$\lambda_p = \dfrac{\lambda}{3}\sqrt{\dfrac{m}{M}}$ , so the answer is (a).

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