# The atomic weight of a newly discovered e ement is 98.225 amu. It has two naturally occuring isotopes. One isotope has a mass of 96.780 amu. The second isotope has a percent abundance of 41.7%. What is the mass of the second isotope?

May 9, 2018

$100.245 \text{amu}$

#### Explanation:

${M}_{r} = \frac{\sum \left({M}_{i} a\right)}{a}$, where:

• ${M}_{r}$ = relative attomic mass ($g$ $m o {l}^{-} 1$)
• ${M}_{i}$ = mass of each isotope ($g$ $m o {l}^{-} 1$)
• $a$ = abundance, either given as a percent or amount of $g$

$98.225 = \frac{96.780 \left(100 - 41.7\right) + {M}_{i} \left(41.7\right)}{100}$

${M}_{i} = \frac{98.225 \left(100\right) - 96.780 \left(58.3\right)}{41.7} = 100.245 \text{amu}$