Question

Atomic mass of most of the elements is fractional. What is the possible reason for this?
A) mass is due to the sum of masses if p, n, e in it which is fractional.
B) average atomic mass of different isotopes of elements.
C) mass of $C - 12$ is in fraction.
D) none of these.

Answer 1

In the above question, it is asked why the atomic mass of most of the elements is fractional. In macroscopic level, most of the elements exist as a mixture of isotopes which though may be radioactive, affect the mass of the atom.

Complete Step by step solution
We know that the atomic mass of an atom depends upon the atomic mass of each of its isotopes. Due to this mixture of the isotopes, the atomic mass is fractional.
Let us take the example of chlorine:
Chlorine has two isotopes chlorine-35 and chlorine 37.
Chlorine-35 has 17 protons and 18 neutrons. And its atomic mass is 35. The percentage of its occurrence is $75\%$ .
Chlorine-37 has 17 protons and 20 neutrons. And its atomic mass is 37. The percentage of its occurrence is $25\%$
So, now we can find the relative atomic mass of Cl as:
${\text{A = }}\sum\limits_{{\text{i = 1}}}^{\text{n}} {{{\text{a}}_{\text{i}}}{{\text{p}}_{\text{i}}}}$
where A = atomic mass of the element
${{\text{a}}_{\text{i}}}$ =atomic mass of ${{\text{i}}^{{\text{th}}}}$ isotope.
${{\text{p}}_{\text{i}}}$ = percentage of occurrence of ${{\text{i}}^{{\text{th}}}}$ isotope.
n= number of isotopes.
Substituting the value of n, we get:
${\text{A = }}\sum\limits_{{\text{i = 1}}}^{\text{2}} {{{\text{a}}_{\text{i}}}{{\text{p}}_{\text{i}}}}$
The average mass will be:
${\text{A = }}{{\text{a}}_{\text{1}}}{{\text{p}}_{\text{1}}}{\text{ + }}{{\text{a}}_{\text{2}}}{{\text{p}}_{\text{2}}}$
Substituting the atomic mass and percentage of occurrence of isotopes of chlorine, we get atomic mass of chlorine as:
${\text{A = 35}} \times \dfrac{{75}}{{100}}{\text{ + 37}} \times \dfrac{{25}}{{100}} = 26.25 + 9.25 = 35.5$
So, we can conclude that the atomic mass of most of the elements is fractional because we take the average atom mass of different isotopes of the element.
So, the correct option is option B.

Note
Elements having no stable isotopes like Francium, radium and actinium, atomic mass is chosen according to the long lived isotopes. So, it is not necessary that elements having isotopes will always have fractional atomic mass.