An electron of mass and magnitude of charge initially at rest gets accelerated by a constant electric field . The rate of change of de-Broglie wavelength of this electron at time ignoring relativistic effects is
Step 1. Given data
Mass of an electron is
Charge on an electron is
Electric field is
Step 2. Finding the de-Broglie wavelength
We know that, the de-Broglie wavelength,
[Where, is the Planck constant, is momentum]
[Where, ] []
Step 3. Finding the velocity
By using the first equation of motion,
[Where, is the initial velocity, is the acceleration, is the time]
[]
By using the formula of the force,
[Where, is the charge, is the electric field.]
[As ]
Putting the value of acceleration in , we get
Step 4. Finding the rate of change of de-Broglie wavelength
Putting the value of velocity in , we get
Now, the rate of change of the de Broglie wavelength is given by differentiating the wavelength with respect to the time
Therefore, the rate of change of the de-Broglie wavelength is
Hence, the correct option is .