Question

The element bromine exists in nature as two isotopes: 79Br has a mass of 78.9183 u, and 81Br has a mass of 80.9163 u. The average atomic mass of bromine is 79.90 u. Calculate the relative abundance (as percentages) of the two bromine isotopes.

Answer 1

Answer:

Abundance of isotope 79Br=51% and abundance of 81Br=49%

Step-by-step explanation:

We are given that

Mass of 79Br=78.9183 u

Mass of 81Br=80.9163 u

Average atomic mass of bromine=79.90 u

We have to find the relative abundance of the two bromine isotopes.

Let x be the abundance of 79Br

Then , abundance of 81Br isotopes=1-x

Average atomic mass=Mass of isotope(abundance of isotope)+Mass of other isotope(abundance of other isotope)

Using the formula

$79.90=78.9183x+(1-x)80.9163$

$79.90=78.9183x+80.9163-80.9163x$

$79.90-80.9163=-1.998x$

$-1.0163=-1.998x$

$x=\frac{1.0163}{-1.998}=0.51$

Percentage of isotope with abundance 0.51=$0.51\times 100=51$%

Abundance of other isotope=1-0.51=0.49

Percentage of other isotope with abundance 0.49=$0.49\times 100=49$%