Final answer:
To determine the atomic mass of the Chromium (Cr) isotope, you need to use the natural abundances and atomic masses of the four isotopes. You can calculate the average atomic mass by multiplying the atomic mass of each isotope by its natural abundance and summing them up.
Step-by-step explanation:
To determine the atomic mass of the Chromium (Cr) isotope, you need to use the natural abundances and atomic masses of the four isotopes. You can calculate the average atomic mass by multiplying the atomic mass of each isotope by its natural abundance and summing them up.
For the ₅₂Cr isotope, with a natural abundance of 83.79% and an atomic mass of 51.9405 u, the contribution to the average atomic mass is (0.8379 x 51.9405 u) = 43.4457 u.
Similarly, for the ₅₄Cr isotope, with a natural abundance of 2.37% and an atomic mass of 53.9389 u, the contribution to the average atomic mass is (0.0237 x 53.9389 u) = 1.2788 u.
The ₅₀Cr and ₅₃Cr isotopes exist in a ratio of 0.4579:1. Let's assume that x is the natural abundance of ₅₀Cr. Then, the natural abundance of the ₅₃Cr isotope would be 0.4579x. We can set up an equation using the sum of the natural abundances to solve for x: x + 0.4579x = 1. Therefore, x = 0.5745.
The contribution of the ₅₀Cr isotope to the average atomic mass is (0.5745 x 49.9460 u) = 28.7002 u.
Now, we can sum up the contributions from each isotope: 43.4457 u + 1.2788 u + 28.7002 u = 73.4247 u. Therefore, the atomic mass of the Chromium isotope is 73.4247 u.