Question

The energy of a photon of sodium light (\(\lambda = 589 \, \text{nm}\)) is equal to the band gap of a semiconducting material. The minimum energy required to create a hole-electron pair is:

• A. \(2.1 \, \text{eV}\)
• B. \(1.1 \, \text{eV}\)
• C. \(6.1 \, \text{eV}\)
• D. \(3.1 \, \text{eV}\)

Hint:

Use the relation E = hc/λ and convert energy from joules to electron volts by dividing by 1.6 × 10−19

Answer 1

The Correct Option is A

The energy of a photon is given by:
\[E = \frac{hc}{\lambda}\]
where $h = 6.626 \times 10^{-34} \text{ J}\cdot\text{s}$, $c = 3 \times 10^{8} \text{ m/s}$, and $\lambda = 589 \text{ nm} = 589 \times 10^{-9} \text{ m}$. Converting $E$ to eV:
\[E = \frac{6.626 \times 10^{-34} \times 3 \times 10^8}{589 \times 10^{-9} \times 1.6 \times 10^{-19}} \approx 2.1 \text{ eV}\]