Question

Two electrons are moving with the same velocity, one electron enters a region of uniform electric field while the other enters a region of uniform magnetic field. Then, after sometime, if the de-Broglie wavelength of two are ${\lambda }_1$ and ${\lambda }_2$ respectively, then

• A. ${\lambda }_1={\lambda }_2$
• B. ${\lambda }_1>{\lambda }_2$
• C. ${\lambda }_1<{\lambda }_2$
• D. ${\lambda }_1>{\lambda }_2$ or ${\lambda }_1<{\lambda }_2$

Answer 1

The correct option is C ${\lambda }_1<{\lambda }_2$

Energy of an electron $E=\frac{hc}{\lambda }$

where, $\lambda$ is the de-Broglie wavelength of the electron.

Therefore, Energy is inversely proportional to the de-Broglie wavelength of an electron.

After some time, electron that has entered electric field has an increase in velocity along the direction of field, which results in the increase of translational kinetic energy without saturation.

The electron which entered the magnetic field has an increased rotational kinetic energy.

Hence, the electron in electric field will have more energy and low de-Broglie wavelenth.

$\Rightarrow {\lambda }_2>{\lambda }_1$

So, the answer is option (C).