Question

The speed of electrons in a scanning electron microscope is $1\times {10}^{7}m{s}^{-1}$. If the proton having the same speed is used instead of electrons, then the resolving power of 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

$1837$

Step 1: Given Data

Speed of electrons $v=1\times {10}^{7}m{s}^{-1}$

The speed of protons is the same as the speed of electrons.

Let the resolving power of protons and electrons be $R{p}_{pr}$ and $R_{el}$ respectively.

Let $h$ be Planck's constant.

Let $p$ be the momentum.

Let $m_{pr}$ and $m_{el}$ be the mass of protons and electrons respectively.

Step 2: Formula Used

Resolving power, $Rp\propto \frac{1}{\lambda }$
Step 3: Calculate the Factor of change

$\lambda =\frac{h}{p}=\frac{h}{mv}\left(\because p=mv\right)$​
$Rp\propto \frac{mv}{h}$​
$\Rightarrow R_P\propto p$
$\Rightarrow R_P\propto mv$
$\Rightarrow R_P\propto m$

Therefore,

$\frac{R{p}_{pr}}{R{P}_{el}}=\frac{m_{pr}}{m_{el}}=\frac{1.672621898\times {10}^{-27}}{9.10938356\times {10}^{-31}}=1837$

Hence, the correct option is C.