There are two naturally occurring isotopes of boron determine the abundance of each isotope

Answer : The correct answer is:

The abundance of isotopes can be found out using following formula:

atomic mass of element = (abundance of isotope 1 * mass of isotope 1) + (abundance of isotope 2 * mass of isotope 2) + ...

Boron (mass = 10.811 u) has two isotopes : ¹⁰B (mass = 10.0129 u) and ¹¹ B (mass = 11.0093 u)

Sum of abundance of all isotopes = 100%

Lets assume abundance of isotope ¹¹B = x % = 0.01 x, so abundance of isotope ¹⁰B = 100 % - x% = 100/100 - x/100 = 1 - 0.01 x

Plugging values in formula:

10.811 = (0.01 x * 11.0093) + [ (1 - 0.01 x) * 10.0129 ]

10.811 = (0.110093 x) + (10.0129 - 0.100129 x)

10.811 - 10.0129 = 0.110093 x - 0.100129 x

0.7981 = 0.009964 x

Dividing both side by 0.00964

0.7981 / 0.009964 = 0.00964 / 0.00964 x

x = 82.7 %

Abundance of of isotope ¹¹ B = 82.7 %

Abundance of isotope ¹⁰ B = 100% - x % = 100 % - 82.7 % = 17.3 %