Question

Electrons used in an electron microscope are accelerated by a voltage of 25 kV. If the voltage is increased to 100 kV then the de-Broglie wavelength associated with the electrons would
1. Increase by 4 times
2. Increase by 2 times
3. Decrease by 2 times
4. Decrease by 4 times

Answer 1

Correct Answer - Option 3 : Decrease by 2 times

CONCEPT: 

• The De Broglie wavelength of an electron accelerated through potential V is given by

\(⇒ λ = \dfrac{h}{mv} = \dfrac{h}{\sqrt{2m \ eV}}\)

Where h = Plancks constant, e = Charge of the electrons, m = mass of the electron, and V = Potential 

CALCULATION :

Given - Electrons voltage = 25 kV ,Voltage is increased to 100 kV

• TheDe Broglie  wavelength of the electron accelerated through a potential 25 kV can be written as

\(⇒ λ = \dfrac{h}{mv} = \dfrac{h}{\sqrt{2m \ e \times 25}}\)

When the potential increased to 100KV. Let the de Broglie wavelength be λ₁ and the equation for  λ1 can be written as

\(⇒ λ_{1} = \dfrac{h}{mv} = \dfrac{h}{\sqrt{2m \ e \times 100}}\)

The above equation can be rewritten as

\(⇒ λ_{1} = \dfrac{h}{mv} = \dfrac{h}{\sqrt{2m \ e \times 25\times 4}}\)

\(\Rightarrow \lambda_{1}= \frac{\lambda }{2}\)

• Hence, option 3 is the answer