Question

The speed of electrons in a scanning electron microscope is $1\times {10}^7{\text{ms}}^{-1}$. If the protons having the same speed are used instead of electrons, then the resolving power of the scanning proton microscope will be changed by a factor of :

• A. $\frac{1}{\sqrt{1837}}$
• B. $\sqrt{1837}$
• C. $1837$
• D. $\frac{1}{1837}$

Answer 1

The correct option is C $1837$

We know that Resolving Power $\left(RP\right)$ of a microscope, $RP\propto \frac{1}{\lambda }$

Also, $\lambda =\frac{h}{p}=\frac{h}{mv}$

So, $\lambda \propto \frac{1}{m}\left(\text{For same speed}\right)$

Hence, $RP\propto m$

$\therefore \frac{R{P}_p}{R{P}_e}=\frac{m_p}{m_e}=\frac{1.673\times {10}^{-27}}{9.109\times {10}^{-31}}=1836.6\approx 1837$