To infer the isotopic abundances for nitrogen, we can make use of the concept of weighted average atomic mass.
The average atomic mass of nitrogen given is 14.01 u. This means that, on average, nitrogen atoms have a mass of 14.01 atomic mass units (u).
Nitrogen has two naturally occurring isotopes: nitrogen-14 (mass = 14.00 u) and nitrogen-15 (mass = 15.00 u). Isotopes are variants of an element that have the same atomic number but differ in the number of neutrons.
To calculate the isotopic abundances of nitrogen, we need to consider that the average atomic mass is a weighted average of the isotopes' masses, where the weights are the relative abundances of each isotope.
Let's represent the isotopic abundance of nitrogen-14 as x (expressed as a decimal) and the isotopic abundance of nitrogen-15 as (1-x). Since the sum of the abundances is equal to 1, the abundance of nitrogen-15 can be represented as (1 - x).
The average atomic mass can be calculated as the sum of the products of each isotope's abundance and mass:
14.01 u = x * 14.00 u + (1 - x) * 15.00 u
Now, we can solve this equation to find the value of x, which represents the isotopic abundance of nitrogen-14:
14.01 u = 14.00 u * x + (15.00 u - 15.00 u * x)
14.01 u = 14.00 u * x + 15.00 u - 15.00 u * x
14.01 u - 15.00 u = - 1.00 u * x
-0.99 u = -1.00 u * x
x = -0.99 u / -1.00 u
x = 0.99
Therefore, we can infer that the isotopic abundance of nitrogen-14 is approximately 0.99 (or 99%) and the isotopic abundance of nitrogen-15 is approximately (1 - 0.99) = 0.01 (or 1%).