Chapter 27, Problem 59P

To determine

The energy associated with the corresponding state

Answer to Problem 59P

Solution:

The energy associated with the corresponding state is $-0.544\text{eV}$

Explanation of Solution

Given:

Angular momentum of a hydrogen atom: $5.273\times {10}^{-34}\text{kg}{\text{.m}}^{\text{2}}\text{/s}$

Formula Used:

$\begin{array}{l}\text{Angular}\text{momentum}\text{(L)}=\frac{nh}{2\pi }\\ E=-\frac{13.6\text{eV}}{n^2}\end{array}$

Calculation:

Firstly, we will calculate the state by the formula $\text{(L)}=\frac{nh}{2\pi }$

$\begin{array}{l}\text{(L)}=\frac{nh}{2\pi }\\ n=\frac{L2\pi }{h}\\ n=\frac{5.273\times {10}^{-34}\text{kg}{\text{.m}}^{\text{2}}\text{/s}\times 2\pi }{6.63\times {10}^{-34}\text{kg}{\text{.m}}^{\text{2}}\text{/s}}=4.99\end{array}$

So, the state is found to be 5 that is n = 5.

Further, the energy of the 5 state can be calculated by using the formula $E=-\frac{13.6\text{eV}}{n^2}$

$E=-\frac{13.6\text{eV}}{n^2}=-\frac{13.6\text{eV}}{5^2}=0.544\text{eV}$

The energy of the 5^th state is $-0.544\text{eV}$.