Question

What is the average atomic mass of gold if half of the gold found in nature has a mass of 197 amu and a half has a mass of 198 amu?

Answer 1

Hint: Before answering the question, we should know that the sum of the masses of the isotopes and then multiply it with the decimal linked with the percent of atoms of that element that are of a given isotope is the average atomic mass of the element.
Average Mass= $\sum (isotope\,mass)\times (percentage\,abundance)$

Complete answer:
The mass of one atom of the element is the Atomic mass. Mass spectrometry helps to measure the atomic mass accurately.
Example: The helium atoms consist of one or two neutrons and both the atoms consist of two protons. They have different masses like 2 or 4 atomic mass units, they are known as isotopes. For an isotope, the mass number is the sum of the number of protons and neutrons that are present in the nucleus of the element. It occurs because every proton and neutron weigh 1 atomic mass unit (amu). The mass of the atom can be calculated by adding the sum of protons and neutrons and multiply it by a unit mass, which means 1 amu. Every element exists as a group of isotopes. The origin of the word isotopes is from the Greek word “isos” (same) and “topes”(place), the elements can be different in the subatomic construction but occupy the same place on the periodic table.
The average atomic mass can be calculated-
Average Mass= $\sum (isotope\,mass)\times (percentage\,abundance)$
Half of the gold found in nature has mass= 197 a.m.u
Therefore, the percentage abundance will be 50%
And the other gold has mass= 198 a.m.u
The remaining percentage abundance will be 50%
Average mass= $(197\times \dfrac{50}{100})$+$(198\times \dfrac{50}{100})$ = 197.5 a.m.u

Note:
How to calculate Average atomic mass:
The average atomic mass of an element= ${{f}_{1}}{{M}_{1}}+{{f}_{2}}{{M}_{2}}...{{f}_{n}}{{M}_{n}}$, Here f represents the natural abundance of the isotope and M represents the mass number of the isotope.
In the periodic table, the average atomic mass is already mentioned under the symbol of the element.
If the data of the natural abundance of many isotopes are given, one can easily calculate the average atomic mass.