Chapter 28.1, Problem 14SSC

To determine

To Find: The radius of first Bohr’s orbit in scale of softball.

Answer to Problem 14SSC

  $1.76\text{ km}$

Explanation of Solution

Given data:

Radius of nucleus of hydrogen atom, $r=1.5\times {10}^{-15}\text{m}$

Radius of softball, $r\text{'}=5\text{cm}\text{=}\text{0}\text{.05}\text{m}$

First orbital radius, $\text{5}{\text{.29×10}}^{\text{-11}}\text{m}$

Calculation:

By scaling:

  $\begin{array}{l}\text{0}\text{.05 m = 1}{\text{.5×10}}^{\text{-15}}\text{m}\\ {\text{1 m = 3×10}}^{\text{-14}}\text{m}\end{array}$

  $\begin{array}{l}{r}_1=\frac{\text{5}{\text{.29×10}}^{\text{-11}}\text{m}}{{\text{3×10}}^{\text{-14}}\text{m}}\\ r_1=\text{1}\text{.76}\times {\text{10}}^3\text{m = 1}\text{.76 km}\end{array}$

Conclusion:

The electron would be located at a distance of $\text{ 1}\text{.76 km}$ which will lie outside the classroom.