Question

The order of magnitude of radius of the nucleus is __________.
A. $10^{-15}$ m
B. $10^{15}$ m
C. $10^{-10}$ m
D. $10^{10}$ m

Answer 1

Hint: The radius of nuclei of an atom is directly proportional to the cube root of the atomic mass of that atom. And a constant is multiplied to make it an inequality having a value of 1.25 fm. So, from the formula, we can find the order of magnitude of the nucleus.

Formulae used:
Nuclear radius, $R={r}_{0}A^{\dfrac{1}{3}}$, where A is the atomic mass number and ${r}_{0}$ is a constant having a value of $1.25\times 10^{-15}$ m.

Complete step-by-step answer:
The nuclear radius of any atom can be approximated by using the formula $R={r}_{0}A^{\dfrac{1}{3}}$, where A is the atomic mass number and ${r}_{0}$ is a constant having a value of $1.25\times 10^{-15}$ m.
So, $R=1.25\times 10^{-15}A^{\dfrac{1}{3}}$, thus the order of magnitude of radius of nucleus is $10^{-15}$.
Hence, option a is the correct answer.

Additional information:
Atomic nucleus is a very small and dense region inside an atom and consists of protons and neutrons. The shape of a nucleus can be spherical, triaxial, pear-shaped or rugby ball-shaped. Nucleus contains almost the whole mass of an atom because of very small contributions from the electron cloud around it. Nuclear force binds together the protons and neutrons to form a nucleus. The diameter of a nucleus is very much smaller than that of an atom.

Note: Approximately a constant density is seen in a stable nucleus, that is why we used the formula of the nuclear radius. Although the constant varies based on the nucleus in question but only about 20 percent variation is seen. So, consideration of the type of nucleus about which the question has been asked is must.