Question

A sample of Element X is found to contain 72.15% of isotope type 1 (84.9118 amu) and 27.85% of isotope type 2 (86.9092 amu). Calculate the average atomic mass.
A
85.13 amu
B
85.47 amu
C
86.21 amu
D
86.49 amu

Answer 1

To calculate the average atomic mass of Element X based on the given isotopic composition, we can use the formula:

\[
\text{Average Atomic Mass} = (f_1 \times m_1) + (f_2 \times m_2)
\]

where:
- \( f_1 \) and \( f_2 \) are the fractional abundances of the isotopes, and
- \( m_1 \) and \( m_2 \) are the masses of the isotopes.

Given:
- Isotope type 1: \( f_1 = 72.15\% = 0.7215 \), \( m_1 = 84.9118 \text{ amu} \)
- Isotope type 2: \( f_2 = 27.85\% = 0.2785 \), \( m_2 = 86.9092 \text{ amu} \)

Now, substituting these values into the formula:

\[
\text{Average Atomic Mass} = (0.7215 \times 84.9118) + (0.2785 \times 86.9092)
\]

Calculating each term:

1. For isotope type 1:
\[
0.7215 \times 84.9118 = 61.162
\]

2. For isotope type 2:
\[
0.2785 \times 86.9092 = 24.194
\]

Now, adding these results together:

\[
\text{Average Atomic Mass} = 61.162 + 24.194 = 85.356 \text{ amu}
\]

Rounding to two decimal places, the average atomic mass is approximately:

\[
85.36 \text{ amu}
\]

Comparing this value with the options provided, the closest match is:

**B. 85.47 amu**.