Question

The energy gap of silicon is $1.14eV.$ 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
$\Delta E=\frac{hc}{\lambda }\text{ or }\lambda =\frac{hc}{\Delta E}$
Here,
$h=6.6\times 10^{-34}J-s,c=3\times 10^{8}m/s,$
$\Delta E=1.14eV=1.14\times 1.6\times 10^{-19}J$
$\therefore \lambda =\frac{6.6\times 10^{-34}\times 3\times 10^8}{1.14\times 1.6\times 10^{-19}}$
$=10.855\times 10^{-7}$
$=10855\mathring{A}$
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 $\lambda =\frac{12375}{\Delta E(eV)}\mathring{A}$