Chapter 29, Problem 19P

To determine

The energy gap .

Answer to Problem 19P

  $\text{1}\text{.1}{\text{×10}}^{\text{6}}$

Explanation of Solution

Given:

Energy gap, ${\text{E}}_{\text{g}}\text{=}\text{0}\text{.72}\text{eV}$ ,

Energy of the photon, $\text{E}\text{=}\text{760}\text{keV}$

Formula used:

It is known that $\text{N=}\frac{\text{hf}}{{\text{E}}_{\text{g}}}$

Where,

  ${\text{E}}_{\text{g}}$ is the energy gap.

  $f$ is frequency

  $N$ is the maximum number of electrons.

  $h$ is Planck’s constant, $6.63\times {10}^{-34}J\cdot s$

Calculation:

The minimum energy provided to an electron must be equal to the energy gap is ${\text{E}}_{\text{g}}\text{=}\text{0}\text{.72}\text{eV}$ .

So, the maximum number of electrons will be $\text{N=}\frac{\text{hf}}{{\text{E}}_{\text{g}}}$

  $\text{=}\frac{\left(\text{760}\text{×}{\text{10}}^{\text{3}}\text{eV}\right)}{\text{0}\text{.72}\text{eV}}\text{=}\text{1}\text{.1}{\text{×10}}^{\text{6}}$

Conclusion:

The required value is $\text{1}\text{.1}{\text{×10}}^{\text{6}}$ .