Q178 / 200 · MHT CET - Medical 2026 (23 April Shift 1) · Physics
In an interference experiment, interference was observed using waves associated with electrons having de-Broglie wavelength $\lambda$. The electrons are produced by using an electron-gun having the potential difference 'V'. To increase the fringe width in an interference pattern,
- Athe slit separation is increased.
- Bthe screen is moved closer to interfering slits.
- Celectron gun voltage be increased.
- Correct answerDelectron gun voltage be decreased.
Solution
Fringe width in an interference pattern is given by $\beta = \dfrac{\lambda D}{d}$
The de-Broglie wavelength of an electron accelerated through a potential difference $V$ is $\lambda = \dfrac{h}{\sqrt{2meV}}$
Substituting the value of $\lambda$, we get $\beta = \dfrac{h D}{d \sqrt{2meV}}$
From the above relation, $\beta \propto \dfrac{1}{\sqrt{V}}$
To increase the fringe width $\beta$, the electron gun voltage $V$ must be decreased. Increasing the slit separation $d$ or moving the screen closer (decreasing $D$) will decrease the fringe width.
Answer: electron gun voltage be decreased.
The de-Broglie wavelength of an electron accelerated through a potential difference $V$ is $\lambda = \dfrac{h}{\sqrt{2meV}}$
Substituting the value of $\lambda$, we get $\beta = \dfrac{h D}{d \sqrt{2meV}}$
From the above relation, $\beta \propto \dfrac{1}{\sqrt{V}}$
To increase the fringe width $\beta$, the electron gun voltage $V$ must be decreased. Increasing the slit separation $d$ or moving the screen closer (decreasing $D$) will decrease the fringe width.
Answer: electron gun voltage be decreased.
Hence, the correct answer is option: 'D'.