Question

A proton and a $L{i}^{3+}$ nucleus are accelerated by the same potential. If ${\lambda }_{Li}$ and ${\lambda }_P$ denote the de Broglie wavelengths of $L{i}^{3+}$ and proton respectively, then the value of $\frac{{\lambda }_{Li}}{{\lambda }_p}$ is $x\times 10^{-}$ 1. The value of $x$ is _______
(Rounded off to the nearest integer) (Mass of $L{i}^{3+}=8.3$ mass of proton)

Answer 1

Answer: 2

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

$\frac{{\lambda }_{Li}}{{\lambda }_p}=\sqrt{\frac{m_p(e)V}{m_{Li}(3e)(V)}}$

$m_{Li}=8.3m_p$

$\frac{{\lambda }_{Li}}{{\lambda }_p}=\sqrt{\frac{1}{8.3\times 3}}=\frac{1}{5}=0.2$

$=2\times 10^{-1}$