2.2 Chromium has four naturally-occurring isotopes: 4.34% of 50Cr, with an atomic weight of 49.9460 amu; 83.79% of 52Cr, with an atomic weight of 51.9405 amu; 9.50% of 53Cr, with an atomic weight of 52.9407 amu; and 2.37% of 54Cr, with an atomic weight of 53.9389 amu. On the basis of these data, confirm that the average atomic weight of Cr is 51.9963 amu.

Average atomic mass = 51.9963 amu

Explanation:

Given dа ta:

Abundance of Cr⁵⁰ with atomic mass = 4.34%, 49.9460 amu

Abundance of Cr⁵² with atomic mass = 83.79%, 51.9405 amu

Abundance of Cr⁵³ with atomic mass = 9.50%, 52.9407 amu

Abundance of Cr⁵⁴ with atomic mass = 2.37%, 53.9389 amu

Average atomic mass = 51.9963 amu

Solution:

Average atomic mass = (abundance of 1st isotope * its atomic mass) + (abundance of 2nd isotope * its atomic mass + ... n) / 100

Average atomic mass = (4.34*49.9460) + (83.79*51.9405) + (9.50*52.9407) + (2.37*53.9389) / 100

Average atomic mass = 216.7656 + 4352.0945 + 502.9367 + 127.8352 / 100

Average atomic mass = 5199.632 / 100

Average atomic mass = 51.9963 amu