Question

A particle of charge $q$, mass $m$ and energy $E$ has de-Broglie wavelength $\lambda$. For a particle of charge $2\, q$, mass $2 \,m$ and energy $2\, E$, the de-Broglie wavelength is

• A. $\frac{\lambda}{4}$
• B. $2 \lambda$
• C. $8 \lambda$
• D. $\frac{\lambda}{2}$

Answer 1

Answer: (D)

The de-Broglie wavelength $\lambda$ of charged particle of charge $q$ mass $m$ and energy $E$ is given by
$\lambda=\frac{h}{\sqrt{2 m E}}\,\,\,...(i)$
For another particle mass $m^{'}=2 \,m$
charge, $q^{'}=2\, q$
and energy, $E^{'}=2 E$
de-Broglie wavelength,
$ \lambda^{'} =\frac{h}{\sqrt{2 m^{'} E^{'}}}$
$ =\frac{h}{\sqrt{2 \times 2 m \times 2 E}} $
$ =\frac{1}{2} \cdot \frac{h}{\sqrt{2 m E}} \lambda^{'}=\frac{\lambda}{2} $