Question

If the mass of one atom is $3.32 \times {10^{ - 23}}g$, then calculate the number of nucleons (neutrons and protons) present in $2$ atoms of the element.
A: $40$
B: $20$
C: $10$
D: $40{N_A}$

Answer 1

Hint: An atom is composed of nucleus and electrons. Protons and neutrons reside in the nucleus. Collectively these are called nucleons. Mass of electrons is negligible compared to the mass of nucleons. So, the mass of atoms is equal to the mass of nucleons of that atom.
Formula used: Molar mass of nucleon$ = 1.6 \times {10^{ - 24}}g$
Number of nucleons in an atom$ = \dfrac{{Mass{\text{ }}of{\text{ }}atom}}{{molar{\text{ }}mass{\text{ }}of{\text{ }}nucleon}} = \dfrac{{Mass{\text{ }}of{\text{ }}atom}}{{1.6 \times {{10}^{ - 24}}}}$

Complete step by step answer:
We know that an atom is composed of nucleus and electrons. Protons and neutrons reside in the nucleus. Collectively these are called nucleons. Mass of an electron is negligible as compared to the mass of nucleons due to which the mass of an atom is approximately equal to the mass of nucleons. Molar mass of the nucleon is $1.6 \times {10^{ - 24}}g$ and the given mass of the atom is $3.32 \times {10^{ - 23}}g$. So, using the formula,
Number of nucleons in an atom$ = \dfrac{{Mass{\text{ }}of{\text{ }}atom}}{{molar{\text{ }}mass{\text{ }}of{\text{ }}nucleon}} = \dfrac{{Mass{\text{ }}of{\text{ }}atom}}{{1.6 \times {{10}^{ - 24}}}}$
We can calculate the number of nucleons in one atom. substituting the given values in above formula,
Number of nucleons in an atom$ = \dfrac{{3.32 \times {{10}^{ - 23}}}}{{1.6 \times {{10}^{ - 24}}}}$
Solving this we get,
Number of nucleons in an atom$ \approx 20$
So, the number of nucleons in one atom is $20$. We have to find the number of nucleons in two atoms. Therefore,
Number of nucleons in two atoms$ = 20 \times 2 = 40$
So the correct answer is option A.


Note:
Mass of the proton is nearly equal to the mass of the neutron but the mass of the neutron is slightly greater than that of the proton. Mass of the proton and neutron is approximately equal to $1.67 \times {10^{ - 24}}g$. This mass is considered to be equal to one atomic mass unit or $1amu$. Protons are positively charged species and neutrons are neutral species.