Question

In an electron microscope the accelerating voltage is increased from 20 kV to 80 kV, the resolving power of the microscope will change from R to

• A. $2R$
• B. $\frac{R}{2}$
• C. $4R$
• D. $3R$

Answer 1

Answer: (A)

$2R$

Electron microscope is a microscope that can magnify very small details with high resolving power due to the use of electrons as the source of illumination. Since the wavelength of electrons are 100,000 times shorter than visible light the electron microscopes have greater resolving power
We have the Abbe's formula as resolution limit $d=\frac{0.61\lambda }{NA}$(NA is the numerical aperture)

The resolving power increases when d, the minimum distance that can be seen between two points in the image, decreases. Thus, according to the formula the resolving power is inversely proportional to the wavelength.

Resolving Power $\propto \frac{1}{\lambda }$

A higher voltage will give the electrons a higher speed. Thus the electrons will have a smaller de Broglie wavelength according to the equation, $\lambda =h/mv$

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

Thus we get Resolving power $\propto \sqrt{V}$

$⟹\frac{R}{R^{\prime }}=\sqrt{\frac{20}{80}}$

Thus, $R^{\prime }=2R$