The ratio of the radii of hydrogen atom and its nucleus is `~ 10^5`. Assuming the atom and the nucleus to be spherical, the ratio of their sizes is

Explanation

To find the ratio of the sizes of a hydrogen atom and its nucleus, we can follow these steps:

### Step 1: Understand the given ratio
We know that the ratio of the radii of the hydrogen atom (R) to its nucleus (r) is given as:
\[ \frac{R}{r} = 10^5 \]

### Step 2: Express the volume of a sphere
The volume \( V \) of a sphere is given by the formula:
\[ V = \frac{4}{3} \pi R^3 \]
For the hydrogen atom, the volume will be:
\[ V_{atom} = \frac{4}{3} \pi R^3 \]
And for the nucleus:
\[ V_{nucleus} = \frac{4}{3} \pi r^3 \]

### Step 3: Substitute the radius of the atom
Since we have \( R = 10^5 r \), we can substitute this into the volume formula for the hydrogen atom:
\[ V_{atom} = \frac{4}{3} \pi (10^5 r)^3 \]

### Step 4: Calculate the volume of the atom
Calculating \( (10^5 r)^3 \):
\[ (10^5 r)^3 = 10^{15} r^3 \]
Thus, the volume of the hydrogen atom becomes:
\[ V_{atom} = \frac{4}{3} \pi (10^{15} r^3) = \frac{4}{3} \pi 10^{15} r^3 \]

### Step 5: Find the ratio of the volumes
Now, we can find the ratio of the volume of the hydrogen atom to the volume of the nucleus:
\[ \frac{V_{atom}}{V_{nucleus}} = \frac{\frac{4}{3} \pi 10^{15} r^3}{\frac{4}{3} \pi r^3} \]

### Step 6: Simplify the ratio
The \( \frac{4}{3} \pi \) and \( r^3 \) terms cancel out:
\[ \frac{V_{atom}}{V_{nucleus}} = 10^{15} \]

### Conclusion
The ratio of the sizes (volumes) of the hydrogen atom to its nucleus is:
\[ \frac{V_{atom}}{V_{nucleus}} = 10^{15} \]