Solved: null Question for NEET

NEET Hard

An electron of mass $m$ with an initial velocity $\vec{V} = V_0 \hat{i}$ ( $V_0 > 0$ ) enters an electric field $\vec{E} = -E_0 \hat{i}$ ( $E_0 = \text{constant} > 0$ ) at $t = 0$ . If $\lambda_0$ is de-Broglie wavelength initially, then its de-Broglie wavelength at time $t$ is

$\lambda_0 t$

$\lambda_0 (1 + \frac{eE_0}{mV_0} t)$

$\frac{\lambda_0}{1 + \frac{eE_0}{mV_0} t}$

$\lambda_0$

Step-by-Step Solution

Initial de-Broglie wavelength $\lambda_0 = \frac{h}{mV_0}$ . The acceleration of the electron is $a = \frac{eE_0}{m}$ . Velocity after time $t$ is $V = V_0 + \frac{eE_0}{m}t$ . The new wavelength $\lambda = \frac{h}{mV} = \frac{h}{m(V_0 + \frac{eE_0}{m}t)} = \frac{h}{mV_0(1 + \frac{eE_0}{mV_0}t)} = \frac{\lambda_0}{1 + \frac{eE_0}{mV_0}t}$ .

Practice Mode Available

Master this Topic on Sushrut

Join thousands of students and practice with AI-generated mock tests.

Get Started