Question

To account for the atomic mass of nitrogen is $ 14.0067$ , what should be the ratio of $ ^{15}N$ and $ ^{14}N$ atoms in natural nitrogen? (Atomic mass of $ ^{14}N = 14.00307u$ and $ ^{15}N = 15.001u$ )

Answer 1

Hint: Atomic mass of any element depends upon its stable isotopes and their abundance in nature. Isotopes are basically defined as the two or more different atoms of the same element which have the same atomic numbers but different mass numbers. So, by using the given atomic masses of two isotopes, we can find out their percentage abundance in nature and then the ratio of atoms of both the isotopes in natural nitrogen.

Complete answer:
We know that Isotopes are basically defined as the two or more different atoms of the same element which have the same atomic numbers but different mass numbers. Atomic mass of any element depends upon its stable isotopes and their abundance in nature.
Atomic mass of $ ^{14}N = 14.00307u$
Atomic mass of $ ^{15}N = 15.001u$
Average atomic mass is $ 14.0067$
First of all we will assume the abundance percentage of both the isotopes as follows:
Let the $ \% $ of $ ^{14}N = x$
$ \% $ of $ ^{15}N = 100-x$
So, the abundance of two isotopes can be calculated using the average atomic mass formula as follows:
$14.0067 = \dfrac{{(x \times 14.00307) + ((100 - x) \times 15.001)}}{{100}}$
$1400.67 = 14.00307x - 15.001x + 1500.1$
Therefore, on solving the above equation, we get:
$x = 99.636$
$ 100-x = 100 - 99.636$
$ 100-x = 0.364$
$ \% $ of $ ^{14}N = 99.636$
$ \% $ of $ ^{15}N = 0.364$
Now, ratio can be calculated as:
$\dfrac{{^{15}N}}{{^{14}N}} = \dfrac{{0.364}}{{99.636}}$
$\dfrac{{^{15}N}}{{^{14}N}} = 0.00365$
Therefore, the answer is $0.00365.$

Note:
We should remember that we can solve these types of questions simply by using the formula for average atomic mass. Average atomic mass of any element is given by adding the multiplication of atomic masses of all the isotopes (stable isotopes) with their percentage abundances in the natural environment.