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## Q. 2.2

Bromine is a red-orange liquid with an average atomic mass of 79.90 amu. Its name is derived from the Greek word bromos (βρoμos), which means stench. It has two naturally occurring isotopes: Br-79 (78.92 amu) and Br-81 (80.92 amu).
What is the abundance of the heavier isotope?

 ANALAYSIS Br-81 mass (80.92 amu); Br-79 mass (78.92 amu) average atomic mass (79.90) Information given: abundance of Br-81 Asked for:

STRATEGY

1. All abundances must add up to 100%
2. Recall the formula relating abundance and atomic mass (Equation 2.1)

(atomic mass $Y_{1}$ ) × $\frac{\% Y_{1}}{100\%}$ + (atomic mass $Y_{2}$ ) × $\frac{\% Y_{2}}{100\%}$ + . . .        (2.1)

atomic mass Y = (atomic mass $Y_{1}$ × $\frac{\% Y_{1}}{100\%}$) + (atomic mass $Y_{2}$ × $\frac{\% Y_{2}}{100\%}$) + . . .

## Verified Solution

 Br-81: x; Br-79: 100 – x 1.  % abundances 79.90 amu = 78.92 amu $\left(\frac{100 – x}{100}\right)$ + 80.92 amu $\left(\frac{ x}{100}\right)$ 2. Substitute into Equation 2.1. 79.90 = 0.7892(100 – x) + 0.8092 x 79.90 = 78.92 – 0.7892 x + 0.8092 x x = 49% 3. Solve for x.

END POINT

The atomic mass of Br, 79.90, is just about halfway between the masses of the two isotopes, 78.92 and 80.92. So, it is reasonable that it should contain nearly equal amounts of the two isotopes.