Question

If the size of a nucleus is 10thpower of -15meters is scales up to the tip of a sharp pin is 10thpower of -5meters ,then what roughly is the size of the atom?

Answer 1

Step 1: Given that:

Size of nucleus = ${10}^{-15}m$

Scaling of the size of the nucleus is up to the tip of the sharp pin.

Size of the tip of the sharp pin = ${10}^{-5}m$

Step 2: Calculation of rough size of the atom:

It is known that the rough size of an atom = ${10}^{-10}m$

Let, in the term of scaling,

k times the size of the nucleus= the size of the tip of the sharp pin

Where k is the scaling factor.

Now,

$k\times {10}^{-15}m={10}^{-5}m$

$\Rightarrow k\times {10}^{-15}={10}^{-5}$

$\Rightarrow k=\frac{{10}^{-5}}{{10}^{-15}}$

$\Rightarrow k={10}^{10}$

Thus,

the scaling factor (k) = ${10}^{10}$

Thus, the rough size of the atom will be

= k time the rough size of the atom

= ${10}^{10}\times {10}^{-10}m$

= ${10}^0$

= $1m$

Hence,

The rough size of the atom will be $1m$ .