JEE Main · 2026 · 04 Apr 2026 · Shift 2 · Modern Physics

The de Broglie wavelength associated with an electron accelerated through a potential difference V is

λ_{e}

and the de Broglie wavelength associated with a proton accelerated through the same potential difference is

λ_{p}

. If their corresponding masses are

m_{e}

and

m_{p}

, respectively, then the ratio of their de Broglie wavelengths

(\frac{λ _{e}}{λ _{p}})

is ______ .

Answer: (A)

Solution

A charge

q

accelerated through

V

gains

q V = \frac{p ^{2}}{2 m}

, so

p = 2 m q V

and

λ = \frac{h}{2 m q V}

. The electron and proton carry the same charge and cross the same potential difference, so

λ \propto \frac{1}{m}

and

\frac{λ _{e}}{λ _{p}} = \frac{m _{p}}{m _{e}}

JEE Main · 2026 · 04 Apr 2026 · Shift 2 · Single correct option