Question

what is the average atomic mass of this element based on the data?
isotope-mass | percent abundance
x-90 | 51.45
x-91 | 11.22
x-92 | 17.15
x-94 | 17.38
x-96 | 2.80
? amu
enter your rounded answer to the hundredths place.

Explanation:

Step1: Recall the formula for average atomic mass

The formula for average atomic mass is the sum of (isotope mass × percent abundance) for each isotope, divided by 100 (since percent abundances are given). Mathematically, it is $\text{Average Atomic Mass} = \frac{\sum (\text{Isotope Mass} \times \text{Percent Abundance})}{100}$.

Step2: Calculate the contribution of each isotope

• For X - 90: $90\times51.45 = 4630.5$
• For X - 91: $91\times11.22 = 1021.02$
• For X - 92: $92\times17.15 = 1577.8$
• For X - 94: $94\times17.38 = 1633.72$
• For X - 96: $96\times2.80 = 268.8$

Step3: Sum up all the contributions

Sum the values from Step 2: $4630.5+1021.02 + 1577.8+1633.72+268.8$.
First, $4630.5+1021.02=5651.52$;
Then, $5651.52 + 1577.8 = 7229.32$;
Then, $7229.32+1633.72 = 8863.04$;
Then, $8863.04 + 268.8=9131.84$.

Step4: Calculate the average atomic mass

Divide the total sum by 100: $\frac{9131.84}{100}=91.3184$.

Step5: Round to the hundredths place

Rounding $91.3184$ to the hundredths place gives $91.32$.

Answer:

91.32