• # question_answer Two electrons are moving with the same speed v. One electron enters a region of uniform electric field while the other enters a region of uniform magnetic field. Then after some time, if the be-Broglie wavelengths of the two are ${{\lambda }_{1}}$and A${{\lambda }_{2}},$then A) ${{\lambda }_{1}}={{\lambda }_{2}}$    B)   ${{\lambda }_{1}}>{{\lambda }_{2}}$    C)   ${{\lambda }_{1}}<{{\lambda }_{2}}$    D)   ${{\lambda }_{1}}<{{\lambda }_{2}}$or${{\lambda }_{2}}<{{\lambda }_{1}}$

The work done by magnetic field is zero, so there is no charge in KE and hence no charge in the magnitude of momentum. The de-Broglie wavelength ${{\lambda }_{2}}$of electron in magnetic field remains the same. The KE of electron in electric field may increase or decrease depending on the angle between the velocity of electron and the electric field. Accordingly, ${{\lambda }_{1}}$may increase or decrease. $\therefore$ ${{\lambda }_{1}}<{{\lambda }_{2}}$or ${{\lambda }_{2}}<{{\lambda }_{1}}$ Hence, the correction option is (d).