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 the concept of average atomic mass and isotopic abundance

The average atomic mass is a weighted - average of the masses of an element's isotopes based on their abundances. Generally, the most abundant isotope contributes the most to the average atomic mass, and the average atomic mass is closest to the mass of the most abundant isotope.

Step2: Analyze the calcium isotopes

The average atomic mass of calcium is approximately 40.08 amu. Among the given calcium isotopes with masses 35.00 amu, 41.00 amu, and 40.00 amu, the mass of 40.00 amu is closest to the average atomic mass of calcium. So the isotope with a mass of 40.00 amu is the most abundant.

Step3: Calculate the average atomic mass of atom X

Use the formula for average atomic mass $A = \sum_{i}m_i\times p_i$, where $m_i$ is the mass of the $i$-th isotope and $p_i$ is its percentage abundance (expressed as a decimal).
For the first isotope of X: $m_1 = 39.946$ amu, $p_1=0.0435$.
For the second isotope of X: $m_2 = 41.941$ amu, $p_2 = 0.8379$.
For the third isotope of X: $m_3 = 42.941$ amu, $p_3=0.0950$.
For the fourth isotope of X: $m_4 = 43.939$ amu, $p_4 = 0.0236$.
$A=(39.946\times0.0435)+(41.941\times0.8379)+(42.941\times0.0950)+(43.939\times0.0236)$
$A = 1.737641+35.124764+4.079395+1.03696$
$A=41.97876$ amu

Answer:

1. The isotope with a mass of 40.00 amu.
2. 41.97876 amu