Chapter 29, Problem 17P

To determine

The longest wavelength.

Answer to Problem 17P

  $1.1\mu m$

Explanation of Solution

Given info:

Energy gap is $1.1eV$ .

Formula used:

  $\lambda =\frac{c}{f}$

Where,

  $\lambda$ is wavelength

  $c$ is speed of light

  $f$ is frequency

The gap energy equals, $E_g=hf=\frac{hc}{\lambda }$

Where,

  $E_g$ is energy gap

  $f$ is frequency

  $\lambda$ is wavelength

  $hf$ is emitted photon

  $h$ is Planck’s constant

  $c$ is speed of light

Calculation:

Photon with the longest wavelength or the minimum frequency for conduction must have an energy equal to energy gap.

Substitute the given value in $\lambda =\frac{c}{f}=\frac{hc}{hf}=\frac{hc}{E_g}$

  $=\frac{\left(1.24\times {10}^{3}eV\cdot nm\right)}{\left(1.1eV\right)}=1.1\times {10}^{3}nm=1.1\mu m$

Conclusion: The required value is $1.1\mu m$ .