Question

The ratio of radius of the nucleus to the radius of the atom is of the order:
A. ${10^5}$
B. ${10^6}$
C. ${10^{ - 5}}$
D. ${10^{ - 6}}$

Answer 1

Hint: In the given question we have to find out which one of the given values would be the right interpretation of the ratio between the nucleus and the atom. Now we know that the radius of the nucleus and the atom is somewhere in the range of ${10^{ - 15}}m$ and ${10^{ - 10}}m$ respectively. Now we just have to solve it and get the answer.

Complete answer:
The given problem statement asks about the approximated ratio that would be obtained when the radius of the nucleus of an atom is being compared to the radius of the entire atom. This won’t give us the exact value but in the range that would be the given option.
Now Dr. Ernest Rutherford was exactly the first to acknowledge this after the gold-foil experiment he conducted. This experiment was the one to state the existence and the comparison of the nucleus.
Now we have to state the radius of both the nucleus and the atom and then we can compare it using the ratio method.
The radius of the nucleus is in the order of : ${10^{ - 15}}m$
The radius of the atom is in the order of :${10^{ - 10}}m$
Now in the next step we just have to solve the values and get the desired ratio :
$
   = \dfrac{{{r_{nucleus}}}}{{{r_{atom}}}} \\
   = \dfrac{{{{10}^{ - 15}}}}{{{{10}^{ - 10}}}} \\
   = {10^{ - 5}} \\
 $
So the desired value is ${10^{ - 5}}$ .

Therefore the right option would be option C, ${10^{ - 5}}$ .

Note:
The Geiger–Marsden experiments (also called the Rutherford gold foil experiment) were a landmark series of experiments by which scientists discovered that every atom has a nucleus where all of its positive charge and most of its mass is concentrated. They deduced this after measuring how an alpha particle beam is scattered when it strikes a thin metal foil