Question

1. gallium has an atomic mass of 69.723 amu. the abundance of ga - 69 (68.926 amu) is 60.11%. what is the atomic mass, in amu, of the other isotope? a) 70.938 amu b) 70.930 amu c) 70.912 amu d) 70.924 amu e) 70.946 amu

Explanation:

Step1: Calculate the abundance of the second isotope

Let the abundance of the first isotope ($Ga - 69$) be $x_1=0.6011$ and its mass be $m_1 = 68.926$ amu. The abundance of the second isotope is $x_2=1 - 0.6011=0.3989$. The average atomic mass of gallium $M = 69.723$ amu.

Step2: Use the formula for average atomic mass

The formula for the average atomic mass $M=x_1m_1 + x_2m_2$. We need to solve for $m_2$. Rearranging the formula gives $m_2=\frac{M - x_1m_1}{x_2}$.
Substitute the values: $M = 69.723$, $x_1 = 0.6011$, $m_1=68.926$ and $x_2 = 0.3989$ into the formula.
$m_2=\frac{69.723-0.6011\times68.926}{0.3989}$
First, calculate $0.6011\times68.926 = 0.6011\times68.926=41.4314186$.
Then, $69.723-41.4314186 = 28.2915814$.
Finally, $m_2=\frac{28.2915814}{0.3989}\approx70.924$ amu.

Answer:

D. 70.924 amu