Question

If the size of an atom (~ 1 Å) were enlarged to the
sile the earth (~107), how large would its
nucleus be? Take size of nucleus - 10 to the po
wer -15​

Answer 1

Correct Question:-

If the size of an atom of diameter nearly $\sf{1\ \AA}$ were enlarged to the size of the earth of diameter nearly $\sf{10^7\ m,}$ how large would its nucleus be? Take diameter of nucleus nearly $\sf{10^{-15}\ m.}$

Solution:-

Let $\sf{x}$ be the diameter of the nucleus when compared to the atom having same size of earth.

We equate the ratio of size of nucleus to that of atom, in general case, and in the case of assumption with earth's size.

Thus we have,

$\sf{\longrightarrow \dfrac{10^{-15}\ m}{1\ \AA}=\dfrac{x}{10^7\ m}}$

$\sf{\longrightarrow \dfrac{10^{-15}\ m}{10^{-10}\ m}=\dfrac{x}{10^7\ m}}$

$\sf{\longrightarrow x=\dfrac{10^{-15}\ m\times10^7\ m}{10^{-10}\ m}}$

$\sf{\longrightarrow x=10^2\ m}$

$\sf{\longrightarrow x=100\ m}$

Thus if the size of an atom is enlarged to the size of the earth, then the size of the nucleus would be as much large in size as a sphere of diameter 100 m.

So the area of cross section of that sphere would be as much large as that of a cricket ground.

The cricket ground is very tiny when compared to the earth or its cross sectional area. Likewise the size of the nucleus would be very small when compared to an atom.