The radius of the two nucleus are in the ratio of 1:2, then the ratio of their mass numbers is:

CONCEPT:

Atom: 

• An atom is composed of three particles, namely, neutrons, protons, and electrons.
  • Hydrogen does not have neutrons.
  • Every atom has a nucleus that bounds one or more electrons around it. The nucleus is composed of protons and neutrons.
  • The protons are positively charged, electrons are negatively charged and neutrons are neutral.

Atomic mass: 

• It is the mass of an atom in a chemical element. It is roughly equivalent to total neutrons and protons present in the atom.
• It is expressed in atomic mass units (denoted by u). 1amu is equal to exactly one-twelfth of the mass of 1 atom of C-12.

CALCULATION:

Given \(\frac{R_{1}}{R_{2}}=\frac{1}{2}\)

We know that the radius of the nucleus is given as,

⇒ R = R0A1/3     ----(1)

Where, A = mass number, R = radius of the nucleus, and Ro = 1.2×10-15 m

So,

\(\Rightarrow R_{1}=R_{o}A_{1}^{1/3}\)     ----(2)

\(\Rightarrow R_{2}=R_{o}A_{2}^{1/3}\)     ----(3)

By dividing equation 2 and equation 3,

\(\Rightarrow\frac{R_{1}}{R_{2}}=\frac{R_{o}A_{1}^{1/3}}{R_{o}A_{2}^{1/3}}\)

\(\Rightarrow \frac{A_{1}}{A_{2}}=\left ( \frac{R_{1}}{R_{2}} \right )^3\)

\(\Rightarrow \frac{A_{1}}{A_{2}}=\frac{1}{8}\)

• Hence, option 1 is correct.