Boron has only two naturally occurring isotopes. The mass of boron-10 is 10.01294 amu and the mass of boron-11 is 11.00931 amu. Calculate the relative abundances of the two isotopes.

Verified step by step guidance

1. Let the abundance of boron-10 be represented as x. Since there are only two isotopes, the abundance of boron-11 will be 1 - x.
2. Set up the equation for the average atomic mass of boron using the given isotopic masses and the variable x for the abundances. The equation will be: (10.01294 amu * x) + (11.00931 amu * (1 - x)) = average atomic mass of boron.
3. Find the average atomic mass of boron from the periodic table, which is typically around 10.81 amu.
4. Substitute the average atomic mass of boron into the equation from step 2 and solve for x.
5. Once x is found, calculate 1 - x to find the abundance of boron-11. The values of x and 1 - x will give the relative abundances of boron-10 and boron-11, respectively.

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, boron has two isotopes, boron-10 and boron-11, which differ in their neutron count. Understanding isotopes is crucial for calculations involving relative abundances and average atomic mass.

Relative Abundance

Relative abundance refers to the proportion of each isotope of an element present in a natural sample. It is typically expressed as a percentage or fraction of the total amount of the element. To calculate relative abundances, one can use the weighted average of the isotopes' masses and their respective contributions to the overall atomic mass of the element.

Weighted Average

A weighted average is a mean that takes into account the varying degrees of importance of the numbers in a data set. In the context of isotopes, the weighted average of the isotopes' masses is calculated using their relative abundances. This concept is essential for determining the average atomic mass of an element based on its isotopes and their respective contributions.