Silicon has three naturally occurring isotopes (Si-28, Si-29, and Si-30). The mass and natural abundance of Si-28 are 27.9769 amu and 92.2%, respectively. The mass and natural abundance of Si-29 are 28.9765 amu and 4.67%, respectively. Find the mass and natural abundance of Si-30.

Verified step by step guidance

1. Step 1: Understand that the average atomic mass of an element is the weighted average of the masses of its isotopes. The weights are the natural abundances of the isotopes. The sum of the natural abundances of all isotopes of an element is 100%.
2. Step 2: Given that the natural abundances of Si-28 and Si-29 are 92.2% and 4.67% respectively, you can calculate the natural abundance of Si-30 by subtracting the sum of the abundances of Si-28 and Si-29 from 100%.
3. Step 3: The mass of Si-30 is not given directly in the problem. However, you can calculate it using the formula for the average atomic mass of Silicon (Si), which is known to be 28.0855 amu. The formula is: Average atomic mass = (mass of Si-28 * abundance of Si-28) + (mass of Si-29 * abundance of Si-29) + (mass of Si-30 * abundance of Si-30).
4. Step 4: You already know the masses and abundances of Si-28 and Si-29, and you've calculated the abundance of Si-30 in step 2. You can rearrange the formula to solve for the mass of Si-30: mass of Si-30 = (Average atomic mass - (mass of Si-28 * abundance of Si-28) - (mass of Si-29 * abundance of Si-29)) / abundance of Si-30.
5. Step 5: Plug the known values into the formula from step 4 to calculate the mass of Si-30. Remember to convert the abundances from percentages to decimals by dividing by 100 before using them in the formula.

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, silicon has three isotopes: Si-28, Si-29, and Si-30, each with distinct masses and natural abundances. Understanding isotopes is crucial for calculating average atomic mass and interpreting elemental properties.

Natural Abundance

Natural abundance refers to the relative proportion of each isotope of an element found in nature, usually expressed as a percentage. In the case of silicon, the natural abundances of Si-28 and Si-29 are given, and the abundance of Si-30 can be determined by subtracting the known abundances from 100%. This concept is essential for calculating the weighted average mass of an element.

Average Atomic Mass

The average atomic mass of an element is calculated by taking the weighted average of the masses of its isotopes, based on their natural abundances. This value reflects the mass of a typical atom of the element as it occurs in nature. To find the average atomic mass of silicon, one must consider the contributions of each isotope's mass multiplied by its natural abundance.