The element nitrogen has an atomic weight of \( \mathbf{1 4 . 0} \) and consists of two stable isotopes nitrogen-14 and nitrogen-15. The isotope nitrogen-14 has a mass of 14.0 amu and a percent natural abundance of \( 99.6 \% \). The isotope nitrogen-15 has a percent natural abundance of \( 0.370 \% \). What is the mass of nitrogen-15?

To find the mass of nitrogen-15 given its natural abundance, we can use the concept of weighted average based on the isotopes and their respective natural abundances. We know the average atomic weight (14.0 amu) is calculated using the formula: \[ \text{Average atomic weight} = ( \text{mass of N-14} \times \text{abundance of N-14} ) + ( \text{mass of N-15} \times \text{abundance of N-15} ) \] We can plug in our known values: - Mass of N-14 = 14.0 amu - Percent abundance of N-14 = 99.6% = 0.996 - Percent abundance of N-15 = 0.370% = 0.00370 Substituting into the equation gives: \[ 14.0 = (14.0 \times 0.996) + (m \times 0.00370) \] This simplifies to: \[ 14.0 = 13.944 + 0.00370m \] Now, subtract 13.944 from both sides: \[ 0.056 = 0.00370m \] Finally, solve for \(m\): \[ m = \frac{0.056}{0.00370} \approx 15.1351 \, \text{amu} \] Thus, the mass of nitrogen-15 is approximately \( 15.1351 \, \text{amu} \).