Question

Bromine has two naturally occurring isotopes (Br-79 and Br-81).

a. Use the periodic table to find the atomic mass of bromine.
b. If the natural abundance of Br-79 is 50.69%, what is the natural abundance of Br-81?
c. If the mass of Br-81 is 80.9163 amu, what is the mass of Br-79?

Answer 1

The relative atomic mass of
`{\rm Br}` is
`79.904`.

The natural abundance of
`{\rm Br}\text{-}79` would be approximately
`49.31\%`.

The mass of
`{\rm Br}\text{-}79` would be approximately
`78.919`.

Step-by-step explanation:

The natural abundance of all naturally occurring isotopes of an element (e.g., bromine) should add up to
`1`. Since the relative abundance of
`{\rm Br}\text{-}81` is
`50.69\%` (
`0.5069`,) the relative abundance of
`{\rm Br}\text{-}79` (the only other naturally occurring isotope of bromine) should be approximately
`1 - 0.5069 = 0.4931`.

The relative atomic mass of an element is the average of the mass of all its isotopes, weighted by the relative abundance of each isotope. It is given that the atomic mass of
`{\rm Br}\text{-}81` is
`80.9163`. If the atomic mass of
`{\rm Br}\text{-}79` is
`x`, the relative atomic mass of
`{\rm Br}` would be:

`(0.5069)\, x + (1 - 0.5069)\, (80.9163)`.

The expression above should be equal to the relative atomic mass of
`{\rm Br}` on the periodic table of elements,
`79.904`. Thus:

`0.5069\, x + (1 - 0.5069)\, (80.9163) = 79.904`.

Solving for
`x` gives:

`\begin{aligned} x &= (79.094 - (1 - 0.5069)\, (80.9163))/(0.5069) \approx 78.919 \end{aligned}`.

Hence, the relative atomic mass of
`{\rm Br}\text{-}79` would be approximately
`78.919`.