Chapter 27, Problem 53P

To determine

The Rydberg constant R using the Bohr Model.

Answer to Problem 53P

Solution:

The value of Rydberg constant R is $1.0974\times {10}^7{\text{m}}^{-1}$.

Explanation of Solution

The value of the Rydberg constant can be calculated by using the formula

$R=\frac{2{\pi }^2{e}^{4}m{k}^2}{h^{3}c}$

By substituting the values of the symbols as

$\begin{array}{c}R=\frac{2{\pi }^2{e}^{4}m{k}^2}{h^{3}c}\\ =\frac{2{\pi }^2{(1.602177\times {10}^{-19}\text{C})}^4(9.109390\times {10}^{-31}\text{kg}){(8.988\times {10}^9\text{N}{\text{.m}}^{\text{2}}{\text{/C}}^{\text{2}})}^2}{{(6.626076\times {10}^{-34}\text{J}\text{.s})}^3(2.997925\times {10}^8\text{m/s})}\\ =1.0974\times {10}^7{\text{m}}^{-1}\end{array}$