Chapter 5.2, Problem 19SSC

Interpretation Introduction

Interpretation:

The 7^th Bohr’s radius of hydrogen atom needs to be compared with the 1^st Bohr’s radius of same atom.

Concept introduction:

According to Bohr’s atomic model, there are different energy levels in an atom where electron can transit with gain or loss of energy. If electron jumps to higher energy level it absorbs some energy, whereas it emits certain energy in the form of radiations when it falls back to lower energy level.

Answer to Problem 19SSC

The 7^thBohr’s radius is 49 times greater than 1^st Bohr’s radius.

Explanation of Solution

Given information:

The Bohr’s theory purposed the radius formula for atoms.

The Bohr radius can be calculated with the equation:

$\text{r = }\frac{{\text{n}}^{\text{2}}{\text{× a}}_{\text{o}}}{\text{Z}}$

Compare the 7^th and 1^st Bohr’s radius:

$\begin{array}{l}{\text{r}}_{\text{1}}\propto \frac{{\text{(1)}}^{\text{2}}}{\text{(1)}}{\text{and r}}_{\text{7}}\propto \frac{{\text{(7)}}^{\text{2}}}{\text{(1)}}\\ \frac{{\text{r}}_{\text{7}}}{{\text{r}}_{\text{1}}}\text{=}\frac{{\text{(7)}}^{\text{2}}}{{\text{(1)}}^{\text{2}}}\text{= 49 times}\end{array}$

Conclusion

The Bohr’s radius depends on atomic number and number of shell.