The element chromium (Cr) consists of four naturally occurring isotopes with atomic masses 49.9460, 51.9405, 52.9407, and 53.9389 u. The relative abundances of these four isotopes are 4.3, 83.8, 9.5, and 2.4%, respectively. From these data, calculate the atomic weight of chromium.

Verified step by step guidance

1. Identify the isotopes of chromium and their respective atomic masses: 49.9460 u, 51.9405 u, 52.9407 u, and 53.9389 u.
2. Identify the relative abundances of each isotope: 4.3%, 83.8%, 9.5%, and 2.4%.
3. Convert the percentage abundances into decimal form by dividing each by 100: 0.043, 0.838, 0.095, and 0.024.
4. Calculate the contribution of each isotope to the atomic weight by multiplying the atomic mass of each isotope by its decimal abundance: (49.9460 u * 0.043), (51.9405 u * 0.838), (52.9407 u * 0.095), (53.9389 u * 0.024).
5. Sum the contributions from all isotopes to find the atomic weight of chromium.

Key Concepts

Isotopes

Isotopes are variants of a chemical element that have the same number of protons but different numbers of neutrons, resulting in different atomic masses. For example, chromium has four isotopes, each with a unique atomic mass, which contributes to the element's average atomic weight based on their relative abundances.

Relative Abundance

Relative abundance refers to the proportion of each isotope of an element present in a sample, usually expressed as a percentage. In the case of chromium, the isotopes have specific relative abundances that must be considered when calculating the weighted average atomic mass of the element.

Weighted Average

The weighted average is a calculation that takes into account the different weights (or contributions) of each component in a dataset. To find the atomic weight of chromium, the atomic masses of its isotopes are multiplied by their respective relative abundances, and the results are summed and divided by 100 to yield the average atomic weight.