Question

if 50.0% of the isotopes of an element have a mass of 136 amu and 50.0% of the isotopes have a mass of 138 amu, what is the average atomic mass of the element?
avg atomic mass = (abundance as a decimal × mass) + ...
options:
a) 134 amu
b) 137 amu
c) 138 amu
d) 136 amu

Explanation:

Step1: Convert percentages to decimals

50.0% as a decimal is \( 0.500 \), and 50.0% is also \( 0.500 \).

Step2: Apply the average atomic mass formula

The formula for average atomic mass is \( \text{Average Atomic Mass} = (\text{Abundance}_1 \times \text{Mass}_1) + (\text{Abundance}_2 \times \text{Mass}_2) \).
Substitute the values: \( (0.500 \times 136) + (0.500 \times 138) \)
First, calculate \( 0.500 \times 136 = 68 \) and \( 0.500 \times 138 = 69 \).
Then, add the results: \( 68 + 69 = 137 \).

Answer:

137 amu (corresponding to the option with 137 amu, e.g., if the options are labeled and one is "137 amu", that's the answer)