If the size of an atom (1Å) were enlarged to the size of the earth (10⁷ m), how large would its nucleus be ? Take size of nucleus = 10⁻¹⁵ m.

The correct option is 100 m.

To find the enlarged size of the nucleus, we need to determine the magnification factor by which the atom is enlarged and then apply this same factor to the nucleus.

First, let's write down the given actual sizes of the atom and the nucleus:
Actual size of the atom, $d_{\text{atom}}=1\text{Å}={10}^{-10}\text{m}$
Actual size of the nucleus, $d_{\text{nucleus}}={10}^{-15}\text{m}$

The atom is enlarged to the size of the Earth:
Enlarged size of the atom, $d_{\text{atom}}^{\text{'}}={10}^7\text{m}$

The magnification factor (scale factor) $M$ of this enlargement is given by the ratio of the enlarged size to the actual size of the atom:
$M=\frac{d_{\text{atom}}^{\text{'}}}{d_{\text{atom}}}=\frac{{10}^7}{{10}^{-10}}={10}^{7-(-10)}={10}^{17}$

Now, we find the enlarged size of the nucleus, $d_{\text{nucleus}}^{\text{'}}$, by multiplying its actual size by the magnification factor $M$:
$d_{\text{nucleus}}^{\text{'}}=d_{\text{nucleus}}\times M$
$d_{\text{nucleus}}^{\text{'}}={10}^{-15}\text{m}\times {10}^{17}={10}^{-15+17}\text{m}={10}^2\text{m}=100\text{m}$

Therefore, if the atom were enlarged to the size of the Earth, its nucleus would be 100 m in size.