In Rutherford's nuclear model of the atom, the nucleus (radius about `10^(-15)m`) is analogous to the sun about which the electron moves in orbit (radius about `10^(-10)m`) like the earth orbits around the sun. If the dimensions of the solar system had the same proportions as those of the atom, would the earth be closer to or further away form the sun than actually it is ? The radius of earth's orbit is about is `1.5xx10^(11)m`. The radius of the sun is taken as `7xx10^8m`.

Explanation

To determine whether the Earth would be closer to or further away from the Sun if the dimensions of the solar system had the same proportions as those of the atom, we can follow these steps:

### Step 1: Understand the Proportions in the Atom
In Rutherford's model:
- The radius of the nucleus (analogous to the Sun) is given as \( r_{nucleus} = 10^{-15} \, \text{m} \).
- The radius of the electron's orbit (analogous to the Earth's orbit) is given as \( r_{electron} = 10^{-10} \, \text{m} \).

### Step 2: Calculate the Ratio of the Electron's Orbit to the Nucleus
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