Dual Nature Of Matter Question 3

Question 3 - 25 January - Shift 1

Electron beam used in an electron microscope, when accelerated by a voltage of $20 kV$. has a de-Broglie wavelength of $\lambda_0$. If the voltage is increased to $40 kV$. then the de-Broglie wavelength associated with the electron beam would be:

(1) $3 \lambda_0$

(2) $9 \lambda_0$

(3) $\frac{\lambda_0}{2}$

(4) $\frac{\lambda_0}{\sqrt{2}}$

Show Answer

Answer: (4)

Solution:

Formula: De Broglie wavelength

When electron is accelerated through potential difference $V$, then

K.E. $=eV$

$\Rightarrow \lambda=\frac{h}{\sqrt{2 m(KE)}}=\frac{h}{\sqrt{2 meV}}$

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

$\therefore \quad \frac{\lambda}{\lambda_0}=\sqrt{\frac{20}{40}}$

$\therefore \lambda=\frac{\lambda_0}{\sqrt{2}}$