Question

Atomic mass of boron is 10.81 amu. It has two isotopes with 80 $%$ and 20 $%$ abundance respectively. The atomic mass of one isotope is 11, the mass of other isotope is:
 (A) 10.81
 (B) 11.01
 (C) 10.05
 (D) 21.82

Answer 1

Hint: The sum of masses of each isotope when multiplied by their natural fractional abundance will give us the average atomic mass. From the formula to find the average atomic mass, with the all given details about isotope 1, we would be able to find the mass of the second isotope.

Complete step by step answer:
- As we know, atoms of the same element can have different numbers of neutrons in their nucleus. These types of atoms which have the same atomic number and different masses are called isotopes.

  -For an isotope, the sum of the numbers of neutrons and protons in the nucleus is called the mass number. This is because of the reason that each proton and each neutron weigh one amu. (atomic mass unit). We can calculate the mass of the atom by adding the number of neutrons and protons and multiplying it by 1 atomic mass unit.
-Another term related to isotopes is the average atomic mass. It is the sum of the masses of an element's isotopes, each multiplied by its natural abundance. Average atomic mass can be given by the equation
Average atomic mass = $\sum\limits_{i=1}^{n}{{{\left( Atomic\text{ }mass\text{ }of\text{ }an\text{ }isotope \right)}_{i}}\times {{\left( Fractional\text{ }abundance \right)}_{i}}}$

Thus, for calculating the average mass we need to first convert percentages into fraction and it can be easily done by dividing the percentage by 100. Then, multiply the mass number for each isotope by the fraction and then add them together.

  - In the given question we are asked to find the mass of the second isotope. Let its value be $x$.
 For the first isotope we are given the following details
 Mass of isotope 1 = 11 amu
 Percentage abundance =80 $%$
  ∴ fractional abundance =0.80
For the second isotope,
Mass of isotope 2 =$x$
Percentage abundance =20 $%$
Fractional abundance = 0.20
 It's given in the question that the average atomic mass of boron is 10.81 amu. Thus, by substituting all these given details in the above equation we get,

 $10.81=\left[ \left( 11\times 0.80 \right)+\left( x\times 0.20 \right) \right]$
 $x$ =10.05
So, the correct answer is “Option C”.

Note: The atomic mass units are used instead of grams because it will allow us to compare more easily the relative atomic masses. The carbon-12 is taken as the reference and an atomic mass unit or amu can be defined as mass equal to one twelfth the mass of an atom of carbon-12.