Chapter 27, Problem 54P

To determine

The Longest wavelength light that can ionize a hydrogen atom.

Answer to Problem 54P

Solution:

The Longest wavelength light that can ionize a hydrogen atom is $91.2\text{nm}$.

Explanation of Solution

Formula Used:

$\lambda =\frac{1.24\times {10}^3\text{eV}\text{.}\text{nm}}{E}$

Calculation:

From the formula $\lambda =\frac{1.24\times {10}^3\text{eV}\text{.}\text{nm}}{E}$, the minimum energy will give the longest wavelength.

So, the minimum energy $13.6\text{eV}$, it is ionization energy.

The Longest wavelength light that can ionize a hydrogen atom can be calculated as

$\begin{array}{l}\lambda =\frac{1.24\times {10}^3\text{eV}\text{.}\text{nm}}{E}\\ \lambda =\frac{1.24\times {10}^3\text{eV}\text{.}\text{nm}}{13.6\text{eV}}\\ \lambda =91.2\text{nm}\end{array}$