Question

In Germanium, the energy gap is about 0.75eV. The wavelength of light which Germanium starts absorbing is
$\begin{array}{l} A.\,5000\mathop {\rm{A}}\limits^ \circ \\\ B.\,1650\mathop {\rm{A}}\limits^ \circ \\\ C.\,16500\mathop {\rm{A}}\limits^ \circ \\\ D.\,165000\mathop {\rm{A}}\limits^ \circ \end{array}$

Answer 1

This question is from the concept of wave nature of light and also semiconductors. Germanium is a natural occurring semiconductor and the value of its energy gap is given to us hence we have to use this and calculate the wavelength of light which it starts absorbing.

Complete step by step answer:
For solving this question, we will use the relation of the wavelength with respect to the energy gap. Relation is given as:
$E = \dfrac{{hc}}{\lambda }$, where h is the Planck’s constant, c is the speed of light in free space, and $\lambda$ is the wavelength of the light.
The value of the Planck’s constant is $6.63 \times {10^{ - 34}}J\,s$
And the value of the speed of light in free space is $3 \times {10^8}m{s^{ - 1}}$
Value of the Energy gap is given in the question. We just have to convert it into joules while calculating.
And the value of wavelength has to be calculated.
Putting all these values in the formula:
$\begin{array}{l} E = \dfrac{{hc}}{\lambda }\\\ \Rightarrow \lambda = \dfrac{{hc}}{E}\\\ \Rightarrow \lambda = \dfrac{{6.63 \times {{10}^{ - 34}} \times 3 \times {{10}^8}}}{{0.75 \times 1.6 \times {{10}^{ - 19}}}}\\\ \Rightarrow \lambda = 16500 \times {10^{ - 10}}\\\ \Rightarrow \lambda = 16500\mathop {\rm{A}}\limits^ \circ \end{array}$
We have calculated the wavelength of light which germanium will start absorbing.

So, the correct answer is “Option C”.

Note:
Question like these are very simple in calculation part but the student has to understand the meaning of the terms in the question to be able to solve it. In this question only one formula was required and the solution was also easy to calculate. Also, this question could be solved if one calculated only the powers of 10 because three out of four options have the same value but the number of powers of 10 are different. In this question many students tend to make mistake about not converting the energy into joules, hence the student should take proper caution about units being in the same unit system.