Question

A p-type semiconductor has acceptor levels 57 $meV$ above the valence band. The maximum wavelength of light required to create a hole is (Planck's constant

h= 6.6×10-34J-s)

• A. $57\AA$
• B. $57\times {10}^{-3}\AA$
• C. $217100\AA$
• D. $11.61\times {10}^{-33}\AA$

Answer 1

Answer: (C)

Step 1: Given that

A p-type semiconductor acceptor levels above the valence band($E$ )= $57meV$

= $57\times {10}^{-3}eV$

= $57\times {10}^{-3}\times 1.6\times {10}^{-19}J$

Planck's constant($h$ )= $6.6\times {10}^{-34}J-s$

Step 2: Calculation of the maximum wavelength of light required to create a hole:

According to Planck's theory,

$E=h\frac{c}{\lambda }$

$\lambda =h\frac{c}{E}$

Therefore,

$\lambda =6.6\times {10}^{-34}J-s\times \frac{3\times {10}^{8}m{s}^{-1}}{57\times {10}^{-3}\times 1.6\times {10}^{-19}J}$

$\lambda =\frac{19.8\times {10}^{-26}}{91.2\times {10}^{-22}}$

$\lambda =0.217100\times {10}^{-4}$

$\lambda =217100\text{Å}$

Therefore,

Option C) 217100 Å is the correct option.