Question

A particle of charge $q$, mass $m$ and energy $E$ has de-Broglie wavelength $\lambda$. For a particle of charge $2q$, mass $2m$ and energy $2E$, 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
$\lambda =\frac{h}{\sqrt{2mE}}...(i)$
For another particle mass $m^{{}^{\prime }}=2m$
charge, $q^{{}^{\prime }}=2q$
and energy, $E^{{}^{\prime }}=2E$
de-Broglie wavelength,
${\lambda }^{{}^{\prime }}=\frac{h}{\sqrt{2m^{{}^{\prime }}{E}^{{}^{\prime }}}}$
$=\frac{h}{\sqrt{2\times 2m\times 2E}}$
$=\frac{1}{2}\cdot \frac{h}{\sqrt{2mE}}{\lambda }^{{}^{\prime }}=\frac{\lambda }{2}$