Chapter 30, Problem 10P

To determine

(a) To determine:

The fraction of mass of hydrogen atom and its nucleus.

Answer to Problem 10P

Solution:

$\frac{m_2}{m_1}=0.9993$

Explanation of Solution

Hydrogen atom consist of an electron and a proton.

Mass of hydrogen atom, $m_1=\text{1}.00\text{79}$

Mass of nucleus, $m_2=1.0072$

$\begin{array}{l}\frac{m_2}{m_1}=\frac{1.0072}{1.0079}=0.9993\\ \frac{m_2}{m_1}=0.9993\end{array}$

To determine

(b) To determine:

Find the fraction of volume of hydrogen atom and its nucleus.

Answer to Problem 10P

Solution:

$\frac{m_2}{m_1}=0.9993$

Explanation of Solution

Calculation:

Volume of hydrogen atom is given by,

$V_1=\frac{4}{3}\pi R^3$

Volume of hydrogen nucleus is given by,

$\begin{array}{l}{V}_2=\frac{4}{3}\pi r^3\\ \frac{V_2}{V_1}=\frac{\frac{4}{3}\pi r^3}{\frac{4}{3}\pi R^3}\\ \frac{V_2}{V_1}=\frac{r^3}{R^3}\\ \frac{V_2}{V_1}=\frac{{(1.25\times {10}^{-15})}^3}{{(53\times {10}^{-12})}^3}\\ \frac{V_2}{V_1}=1.311\times {10}^{-14}\end{array}$