Question

Chromium has an atomic mass of 51.9961 u and consists of four isotopes, 50 Cr, 52Cr, 53 Cr, and 54 Cr. The 52 Cr isotope has a natural abundance of 83.79% and an atomic mass of 51.9405 u. The 54 Cr isotope has a natural abundance of 2.37% and an atomic mass of 53.9389 u. The natural abundances of the 50 Cr and 53 Cr isotopes exist in a ratio of 1:0.4579, and the 50Cr isotope has an atomic mass of 49.9460 u. Determine the atomic mass of the "Cr isotope. atomic mass of 53 Cr: 56.4961

Answer 1

The ratio of the natural abundances of Cr and "Crisotopes is 1:0.4579. Let x% be the natural abundance of "Cr. The natural abundance of 5°Сr will be 0.4579x %. The sum of natural abundances of all the isotopes is 100 83.79+2.37+x+0.4579x =100 86.16+1.4579x = 100 1.4579x = 100-86.16 1.4579x = 13.84 13.84 x= 1.4579 = 9.4931 0.4579x = 0.4579(9.4931) = 4.3469 Cr and Crisotopes are 4.3469% and 9.4931% Hence, the natural abundances of respectively.

The formula for the average atomic mass of chromium is as shown below: ΣΜx A Average atomic mass of Cr=2" Here, Mis the atomic mass of a particular isotope and A is its natural abundance. Let y u be the atomic mass of "Cr isotope.

MXA Average atomic mass of Cr= 51.9405 ux 83.79+53.9389 u x 2.37+49.9460 u x 4.3469+ yux9.4931 51.9961 u = 83.79+2.37+9.4931+4.3469 4352.094 +127.8352 +217.1099 +9.4931y 51.9961= 100 51.9961x100 = 4352.094 +127.8352 +217.1099+9.4931y 5199.61 = 4697.04 +9.4931y 9.4931 y = 5199.61-4697.04 = 502.5704 502.5704 9.4931 = 52.9406 u V Hence, the atomic mass of " Cr isotope is 52.9406 u.