Question

What is the atomic mass of hafnium if, out of every 100 atoms, 5% have a mass of 176, 19% have a mass of 177.0, 27% have a mass of 178.0, 14% have a mass of 179.0, and 35% have a mass of 180.0?

A. 178.8 amu

B. 179.1 amu

C. 177.5 amu

D. 179.8 amu

Answer 1

To find the atomic mass of hafnium, we calculated a weighted average based on the given isotopic masses and their relative abundances. The result was 178.55 amu, which does not match any of the provided answer choices exactly.

Step-by-step explanation:

To calculate the atomic mass of hafnium, we will need to use the given percentages and isotopic masses to find a weighted average. Here is the provided information in the question:
5% have a mass of 176 amu
19% have a mass of 177.0 amu
27% have a mass of 178.0 amu
14% have a mass of 179.0 amu
35% have a mass of 180.0 amu

To find the atomic mass, we multiply the mass of each isotope by its relative abundance (percentage), and then sum all these values:

1. 0.05 x 176 = 8.8
2. 0.19 x 177 = 33.63
3. 0.27 x 178 = 48.06
4. 0.14 x 179 = 25.06
5. 0.35 x 180 = 63.0

Adding these values together gives us the average atomic mass:

8.8 + 33.63 + 48.06 + 25.06 + 63 = 178.55 amu

Looking at the provided options, none exactly matches the calculated value of 178.55 amu, so it seems like there might be a typo in the question or answer choices.