Question

Naturally occurring gallium consists of two isotopes. One of those isotopes is 71Ga with an isotopic mass of 70.9247050 amu and an abundance of 39.892%. What is the mass number of the other isotope?

Answer 1

The mass number of the other isotope of naturally occurring gallium is approximately 42.848.

Step-by-step explanation:

The atomic mass of an element is the weighted average of the masses of its isotopes, taking into account their abundances. In the case of naturally occurring gallium, one isotope is 71Ga with an abundance of 39.892%. To find the mass number of the other isotope, we subtract the abundance of 71Ga from 100% (since the total abundance must add up to 100%), which gives us 60.108%. The mass number of the other isotope can be calculated by dividing this abundance by 100 and multiplying by the isotopic mass of 70.9247050 amu for 71Ga. This gives us a result of approximately 42.848.

Answer 2

The answer is 69.

Relative atomic mass of an element is a sum of the products of each isotopic mass and its abundance. We first need to calculate the isotopic mass of the second isotope to find out its mass number.

So,
- the isotopic mass of the first isotope: Ar1 = 70.9247050 amu
- the abundance of the first isotope: a1 = 39.892% = 0.39892
- the abundance of the second isotope a2 = 100% - a1 = 100% - 39.892% = 60.108% = 0.60108
- the isotopic mass of the second isotope is unknown: Ar2 = ?

Thus, using the formula:
Ar(Ga) = Ar1 * a1 + Ar2 * a2
69.723 = 70.9247050 * 0.39892 + Ar2 * 0.60108
69.723 = 28.2932833186 + 0.60108 Ar2
0.60108 Ar2 = 69.723 - 29.2832833186 = 41.4297166814
Ar2 = 41.4297166814 / 0.60108 = 68.92546197078592 amu ≈ 69 amu

Since the isotopic mass of the second isotope is ≈ 69 amu, the mass number of the isotope is 69.