question_answer

An electron is confined to a tube of length L. The electron?s potential energy in one half of the tube is zero, while the potential energy in the other half is 10 eV. If the electron has a total energy \[E=15\,\,eV\], then the ratio of the de- Broglie wavelength of the electron in the 10 eV region of the tube to that in the other half is-

A) \[1/\sqrt{3}\]                 

B) \[\sqrt{3}\]

C) \[3\]                             

D) \[\frac{1}{3}\]

Correct Answer: B

Solution :

Kinetic energy \[{{k}_{2}}=15-10\,\,=\,\,5\,\,eV\] Tube \[KE\text{ }in\text{ }other\text{ }region\,\,=\,\,15\text{ }V.\] \[\frac{{{\lambda }_{1}}}{{{\lambda }_{2}}}\,\,=\,\,\sqrt{\frac{{{k}_{2}}}{{{k}_{1}}}}\,\,\Rightarrow \,\,\frac{{{\lambda }_{10V}}}{{{\lambda }_{0}}}\,\,\sqrt{\frac{15}{5}}\,\,=\,\,\sqrt{3}\]