The energy of a photon of sodium light of wavelength \( 589 \) nm is equal to the energy gap of a semiconducting material. The minimum energy required (in eV) to create a hole-electron pair will be
(Take \( h = 6.63\times10^{-34} \) J s; \( c = 3\times10^{8} \) m \( \mathrm{s^{-1}} \); \( e = 1.6\times10^{-19} \) C)
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \( \sim 2.1 \)
The minimum energy needed to create an electron–hole pair is the energy gap \( E_{g} \), which here equals the photon energy \( E = hc/\lambda \) of the sodium light.
\( \lambda = 589\,\mathrm{nm} = 589\times10^{-9}\,\mathrm{m} \)
\( \displaystyle E = \frac{hc}{\lambda} = \frac{(6.63\times10^{-34})(3\times10^{8})}{589\times10^{-9}}\,\mathrm{J} = 3.377\times10^{-19}\,\mathrm{J} \)
\( \displaystyle E = \frac{3.377\times10^{-19}}{1.6\times10^{-19}}\,\mathrm{eV} \approx 2.11\,\mathrm{eV} \approx 2.1\,\mathrm{eV} \)
Shortcut: With \( hc \approx 1240\,\mathrm{eV\,nm} \): \( E = 1240/589 \approx 2.1 \) eV.