Electron are accelerated through a potential difference V and protons are accelerated through a potential difference of 4 V . The de - Broglie wavelengths are λ e a n d λ p for electrons and protons,

Question

Electron are accelerated through a potential difference V and protons are accelerated through a potential difference of 4 V . The de - Broglie wavelengths are λ e a n d λ p for electrons and protons, respectively. The ratio of λ e λ p is given by (given, m e is mass of electron and m p is mass of proton)

TestHub · Accepted Answer

We have, E = q V , we know that E = 1 2 m v 2 ⇒ v = 2 E m As, λ = h m v = h m 2 E m ⇒ λ = h 2 m q V .... (i) For electron, λ e = h 2 m e e V .... (ii) For proton, λ p = h 2 m p e V ′ ∵ q = e ∴ λ p = h 2 m p q . 4 V ∵ V ′ = 4 V ... (iii) On dividing equation (ii) by equation (iii), we get λ e λ p = 2 m p m e

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