Physics - Modern Physics Question with Solution | TestHub

Force on the electron is $F=eE$

Acceleration of the electron is $a=\frac{F}{m}=\frac{eE}{m}$

Velocity of the electron at time $t$ is $v=u+at=\frac{eEt}{m}$

The de-Broglie wavelength of the electron is $\lambda =\frac{h}{mv}$

Substituting the value of $v$, we get $\lambda =\frac{h}{m\left(\frac{eEt}{m}\right)}=\frac{h}{eEt}$

The rate of change of de-Broglie wavelength is $\frac{d\lambda }{dt}=\frac{d}{dt}\left(\frac{h}{eEt}\right)=-\frac{h}{eE{t}^2}$

Answer: $-\frac{h}{eE{t}^2}$