Question

1. calcium has three different isotopes. one has a mass of 35.00 amu; another has a mass of 41.00 amu; and another has a mass of 40.00 amu. which isotope is the most abundant of the three?
2. several isotopes of a certain atom “x” exist. 4.35% of all x atoms have a mass of 39.946 amu. 83.79% have a mass of 41.941 amu, 9.50% have a mass of 42.941 amu, and 2.36% have a mass of 43.939 amu. what is the average atomic mass of atom x?

Explanation:

Step1: Recall average atomic mass formula

The average atomic mass ($A_{avg}$) of an element with isotopes is calculated as $A_{avg}=\sum_{i} (m_i\times p_i)$, where $m_i$ is the mass of the $i$-th isotope and $p_i$ is the percent - abundance of the $i$-th isotope (expressed as a decimal).

Step2: Convert percentages to decimals

For the first isotope: $p_1 = 0.8379$, $m_1=41.941$ amu; for the second isotope: $p_2 = 0.0435$, $m_2 = 39.946$ amu; for the third isotope: $p_3=0.0950$, $m_3 = 42.941$ amu; for the fourth isotope: $p_4=0.0236$, $m_4 = 43.939$ amu.

Step3: Calculate the contribution of each isotope

The contribution of the first isotope is $m_1\times p_1=41.941\times0.8379 = 35.123$ amu.
The contribution of the second isotope is $m_2\times p_2=39.946\times0.0435 = 1.738$ amu.
The contribution of the third isotope is $m_3\times p_3=42.941\times0.0950 = 4.079$ amu.
The contribution of the fourth isotope is $m_4\times p_4=43.939\times0.0236 = 1.037$ amu.

Step4: Calculate the average atomic mass

$A_{avg}=35.123 + 1.738+4.079 + 1.037=41.977$ amu.

Answer:

41.977 amu