Question

If Bromine atom is available in the form of, say, two isotopes ${}_{35}{}^{79}\mathrm{Br}$ (49.7%) and ${}_{35}{}^{81}\mathrm{Br}$ (50.3%), calculate the average atomic mass of Bromine atom.

Answer 1

Step 1: Contribution toward atomic mass

Given that isotope of Bromine with the atomic mass, 79u has 49.7% composition.

And also the isotope of Bromine with the atomic mass, 81u has 50.3% composition.

$\therefore$contribution of ${}_{35}{}^{79}\mathrm{Br}$ towards the atomic mass is

$$\begin{gathered} \frac{\left(79\times 49.7\right)}{100} \\ =\frac{3926.3}{100} \\ =39.263 \end{gathered}$$

$\therefore$contribution of ${}_{35}{}^{81}\mathrm{Br}$ towards the atomic mass is

$$\begin{gathered} \frac{\left(81\times 50.3\right)}{100} \\ =\frac{4074.3}{100} \\ =40.743 \end{gathered}$$

Step 2: Finding average mass

Now combining both the contribution of ${}_{35}{}^{79}\mathrm{Br}$ and ${}_{35}{}^{81}\mathrm{Br}$ we get the average atomic mass:

$$\begin{gathered} \mathrm{Average}\mathrm{atomic}\mathrm{mass}=39.263+40.743 \\ \mathrm{Average}\mathrm{atomic}\mathrm{mass}=80.006\mathrm{u} \end{gathered}$$

Therefore, the average atomic mass of the Bromine atom is $80.006\mathrm{u}$