Question

In a $p$ - type semiconductor the donor level is at $50 \,meV$ above the valence band. To produce one electron, the maximum wavelength of light photon required is (Planck's constant, $h=6.6 \times 10^{-34} \,Js$ and speed of light in vacuum, $c=3 \times 10^{8} \,ms ^{-1}$ )

• A. $0.0248\, \mu m$
• B. $0.248 \, \mu m$
• C. $2.48 \, \mu m$
• D. $24.8\, \mu m$

Answer 1

The Correct Option is D

Given,
$p$ -type semiconductor donor energy level,
$E=50\, meV =50 \times 10^{-3} \times 1.6 \times 10^{-19} \,V$
Planck's constant, $h=6.6 \times 10^{-34} \,Js$
speed of light in vacuum, $c=3 \times 10^{8} \,m / s$
Now, for the maximum wavelength of light photon's required $(p)$.
According to the Planck's quantum theory,
$\therefore \, E=h v $
$\Rightarrow E=\frac{h c}{\lambda} $
$\left[\because v=\frac{c}{\lambda}\right]$
Putting the given values, we get
$50 \times 10^{-3} \times 1.6 \times 10^{-19}=\frac{6.6 \times 10^{-34} \times 3 \times 10^{8}}{\lambda} $
$ \lambda= \frac{6.6 \times 10^{-34} \times 3 \times 10^{8}}{50 \times 10^{-3} \times 1.6 \times 10^{-19}} $
$= \frac{6.6 \times 3 \times 10^{-34} \times 10^{8}}{5 \times 16 \times 10^{-22}}=\frac{6.6 \times 3 \times 10^{-4}}{5 \times 16} $
$=2.475 \times 10^{-5} \,m$
or $\lambda=24.75 \times 10^{-6}=24.75 \,\mu m$
Hence. the maximum wavelength of light photon required is $24.8\, \mu \,m$