Question

The atomic mass of boron is 10.81. It has two isotopes with an abundance of 80% and 20% respectively. The atomic mass of the isotope having 80% abundance is 11.01. The atomic mass of other isotopes is:

A. 10.81

B. 11.01

C. 10.01

D. 21.82

Answer 1

Hint: To answer this question, we should know the formula for average atomic mass. The average atomic mass of an element is the sum of the masses of its isotopes, each multiplied by its natural abundance.

Complete step-by-step answer:

We should know that an element can have differing numbers of neutrons in its nucleus, but it always has the same number of protons. The versions of an element with different neutrons have different masses and are called isotopes. In short, we can say that isotopes have different atomic masses and the same atomic number.

\[Average\text{ }atomic\text{ }mass~=\dfrac{(Atomic\,mass\times ~percentage~abundance~of~1)+(Atomic\,mass\times ~percentage~abundance~of~2)}{100}\]

It is given that:

The average atomic mass of boron= 10.81

Percentage abundance of first boron isotope= 80%

The atomic mass of the first boron isotope having 80% abundance= 11.01

Percentage abundance of second boron isotope=20%

The atomic mass of second boron isotope with 20% abundance= x

Putting these values in the above formula:

 $10.81~=\dfrac{(11.01\times ~80~)+(x\times ~20)}{100} $

 $ 10.81\times 100=880.8+20x $

 $\dfrac{1081-880.8}{20}=x $

  x=10.01 

So, from the above calculation we came to know the correct answer of this option C.

Note: We should note that the exact mass of an isotope is something that is determined experimentally. To find the average atomic mass experimentally a mass spectrometer is used. This laboratory instrument works based on the differences in the mass of the different isotopes of an element. Because isotopes for an element have different masses, they can be separated, and the percentage of each isotope is measured. From these measurements, the average atomic mass can be calculated.