Question

Two electrons are moving with same speed $v$. One electron enters a region of uniform electric field while the other enters a region of uniform magnetic field, when after some time de Broglie wavelengths of two are ${\lambda }_1$ and ${\lambda }_2$, respectively. Now :

• A. ${\lambda }_1={\lambda }_2$
• B. ${\lambda }_1>{\lambda }_2$
• C. ${\lambda }_1<{\lambda }_2$
• D. ${\lambda }_1$ can be greater than or less than ${\lambda }_2$

Answer 1

The correct option is D ${\lambda }_1$ can be greater than or less than ${\lambda }_2$

In a uniform electric field, an electron has a motion with uniform acceleration in the direction of the field with a magnitude which equals $\frac{eE}{m_e}$ whereas in a uniform magnetic field, an electron undergoes a circular motion with the centripetal force of magnitude $evB$. Since the motion is circular in the magnetic field the magnitude of the velocity of the electron will be equal to the initial velocity of $v$.

$\therefore$ ${\lambda }_2=\frac{h}{mv}$

But in the case of the uniform electric field, the final velocity depends on the direction of the electric field and the time period for which it is applied. If the applied field is opposite to the initial direction then the final velocity could be zero which means ${\lambda }_1>{\lambda }_2$ whereas if the applied field is in the direction of initial motion then ${\lambda }_1<{\lambda }_2$ after some time.