Question

The de Broglie wavelength of an ­electron accelerated through a potential difference ‘V’ is_____________.
1. 0.202/^√V) oA
2. (0.101/^√V ) oA
3. (12.27/^√V ) oA
4. (1.227/^√V) oA

Answer 1

Correct Answer - Option 3 : (12.27/^√V ) oA

CONCEPT:

• The wavelength of the electron due to its motion is called the de-Broglie wavelength of the electron and is given by

\(\lambda = \frac{h}{P}\)

• The de Broglie wave equation explains the dual nature of matter as it connects the wave characteristics, λ to particle characteristics P.
• The bundle of light rays is called a photon.

EXPLANATION :

• The de-Broglie wavelength of an electron (λe) is given by:

\({\lambda _e} = \frac{h}{{\sqrt {2m\;E} }}\)

Where h = Plancks constant, m = mass of the particle, V = Velocity

• Substituting the values of m,E,h in the abive equation the wavelength of an electron accelerated through a potential V is given by 

\(λ =\frac{12.27}{\sqrt{V}}\)

• Hence, option 4 is the answer