3) gallium has an atomic mass of 69.723 amu. the abundance of ga - 69 (68.926 amu) is 60.11%. what is the…

3) 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

3) 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

Answer

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