Question

The energy gap of silicon is $1.14\, eV.$ The maximum wavelength at which silicon will begin absorbing energy is:

• A. $ 18.855\,\mathring{A}$
• B. $ 108.55\,\mathring{A}$
• C. $ 1085.5\,\mathring{A}$
• D. $ 10855\,\mathring{A}$

Answer 1

Answer: (D)

Energy absorbed by silicon is given by
$\Delta E=\frac{h c}{\lambda} \text { or } \lambda=\frac{h c}{\Delta E}$
Here,
$h =6.6 \times 10^{-34} J - s , c=3 \times 10^{8} m / s ,$
$\Delta E =1.14 \,eV =1.14 \times 1.6 \times 10^{-19} J$
$\therefore \lambda =\frac{6.6 \times 10^{-34} \times 3 \times 10^{8}}{1.14 \times 1.6 \times 10^{-19}} $
$=10.855 \times 10^{-7} $
$=10855 \mathring{A}$
Note : After putting the values of $h$ and $c$ in the expression for energy, we get
$\Delta E=\frac{12375}{\lambda(\mathring{A})} eV$
or $\lambda=\frac{12375}{\Delta E( eV )} \mathring{A}$