NEET 2025 — Physics solution

NEET2025Physics

A photon and an electron (mass $m$ ) have the same energy $E$ . The ratio $(λ_{p h o t o n} / λ_{e l ec t r o n})$ of their de-Broglie wavelengths is ( $c$ is the speed of light):

A
$\frac{E}{2 m}$
B
$c 2 m E$
C
$c \frac{2 m}{E}$
D
$\frac{1}{c} \frac{E}{2 m}$

Solution

Photon: $E = h c / λ_{p h o t o n} \Rightarrow λ_{p h o t o n} = h c / E$ .

Electron (non-relativistic): $E = p^{2} / (2 m) \Rightarrow p = 2 m E$ , so $λ_{e l ec t r o n} = h / 2 m E$ .

$\frac{λ _{p h o t o n}}{λ _{e l ec t r o n}} = \frac{h c / E}{h / 2 m E} = \frac{c 2 m E}{E} = c \frac{2 m}{E}$ .

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