Question

Two particles of mass $m$ and $2m$ have equal kinetic energy. Their De Broglie wavelengths are in the ratio:

• A. $1:1$
• B. $1:2$
• C. $1:\sqrt{2}$
• D. $\sqrt{2}:1$

Answer 1

The correct option is D $\sqrt{2}:1$

As we know,

$\lambda =h/mv$

$\lambda =\frac{h}{\sqrt{2mE}}$

as the kinetic energy of both particles are same so

$\lambda \propto \frac{1}{\sqrt{m}}$

$\frac{{\lambda }_1}{{\lambda }_2}=\frac{\sqrt{2}}{1}$