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. $=eV$
$\Rightarrow \lambda=\frac{h}{\sqrt{2 m(KE)}}=\frac{h}{\sqrt{2 meV}}$
$\therefore \quad \lambda \propto \frac{1}{\sqrt{V}}$
$\therefore \quad \frac{\lambda}{\lambda_0}=\sqrt{\frac{20}{40}}$
$\therefore \lambda=\frac{\lambda_0}{\sqrt{2}}$
