To calculate the average atomic mass of hydrogen based on its isotopic abundances, you can use the following formula:
\[ \text{Average atomic mass} = \sum ( \text{isotopic mass} \times \text{fractional abundance}) \]
Given:
- For \( ^1H \) (protium), the mass is approximately 1.00784 u and its abundance is 99% or 0.99.
- For \( ^2H \) (deuterium), the mass is approximately 2.01410 u and its abundance is 0.8% or 0.008.
Now, apply the values:
\[ \text{Average atomic mass} = (1.00784 , \text{u} \times 0.99) + (2.01410 , \text{u} \times 0.008) \]
Calculating each term:
-
For \( ^1H \): \[ 1.00784 , \text{u} \times 0.99 = 0.99776 , \text{u} \]
-
For \( ^2H \): \[ 2.01410 , \text{u} \times 0.008 = 0.0161128 , \text{u} \]
Now, add these two results together:
\[ \text{Average atomic mass} = 0.99776 , \text{u} + 0.0161128 , \text{u} = 1.0138728 , \text{u} \]
Rounded to a reasonable number of significant figures, the average atomic mass of hydrogen is approximately:
\[ \text{Average atomic mass} \approx 1.014 , \text{u} \]