Chapter 28.1, Problem 13SSC

To determine

To Find: Radiation’s wavelength and where the electromagnetic radiation lies in the spectrum.

Answer to Problem 13SSC

  $\text{2}\text{.067 cm}$ , Microwave region

Explanation of Solution

Given data:

For 101^th energy level, $n_{101}=101$

For 100^th energy level, $n_{100}=100$

Formula used:

Energy of hydrogen atom in energy level n can be:

  $E\left(n\right)=\frac{-1}{n^2}\times 13.6\text{eV}$

Wavelength of the radiation can be obtained by:

  $E=\frac{\text{1240 }\text{eV}\cdot \text{nm}}{\lambda }$

Calculation:

For 101^th energy level, $n_{101}=101$

  $E_{101}=\frac{1}{{101}^2}\times \left(-13.6\right)=-0.0013\text{eV}$

For 100^th energy level, $n_{100}=100$

  $E_{100}=\frac{1}{{100}^2}\times \left(-13.6\right)=-0.00136\text{eV}$

Energy difference:

  $E_{100}-E_{101}=-0.00136\text{eV}-\left(-0.0013\text{eV}\right)=-0.00006\text{eV}$

Wavelength of the radiation:

  $\begin{array}{l}\lambda =\frac{\text{1240 }\text{eV}\cdot \text{nm}}{E}\\ \lambda =\frac{\text{1240 }\text{eV}\cdot \text{nm}}{0.00006\text{eV}}=2.067\times {10}^7\text{nm = 2}\text{.067 cm}\end{array}$

This lies in the microwave region.

Conclusion:

Radiation’s wavelength is $\text{ 2}\text{.067 cm}$ and this lies in the microwave region.