Question

What is the atomic mass of hafnium if, out of every $$100$$ atoms, $$5$$ have a mass of $$176$$, $$19$$have a mass of $$177$$, $$27$$have a mass of $$178$$, $$14$$have a mass of $$179$$, and $$35$$ have a mass of a $$180$$?

Answer 1

Hint: In chemistry, periodic tables play a vital role. In the periodic table totally $$118$$ elements. In the periodic table totally $$18$$ columns and $$7$$ rows. The columns are called as groups. Hence, $$18$$ groups in the periodic table. The rows are called periods. Hence, the total $$7$$ period in the table.
Formula used: The average atomic mass of the atom is defined as the average of the atomic mass of the atom with respect to their percentage in nature.
Average atomic mass is equal to the sum of the product mass of atom respect that counts in percentage.
$$\text{average atomic mass = }{\displaystyle \frac{\text{atomic weight of the atom times number of atoms count}}{\text{100}}}$$

Complete step by step answer:
Given,
In hafnium out of $$100$$ atom,
The number of atoms with a mass of $$176$$ is $$5$$.
The number of atoms with a mass of $$177$$ is $$19$$.
The number of atoms with a mass of $$178$$ is $$27$$.
The number of atoms with a mass of $$179$$ is $$14$$.
The number of atoms with a mass of $$180$$ is $$35$$.
The average atomic mass of the given data of hafnium is,
$$\text{average atomic mass = }{\displaystyle \frac{\text{atomic weight of the atom times number of atoms count}}{\text{100}}}$$
Now we can substitute the known values we get,
$$={\displaystyle \frac{(176\times 5)+(177\times 19)+(178\times 27)+(179\times 14)+(180\times 35)}{100}}$$
$$=\frac{17855}{100}$$
On simplification we get,
$$=178.55$$
The mass of hafnium in above calculation is $$178.55g$$
Hence, the atomic mass of hafnium if, out of every $$100$$ atoms, $$5$$ have a mass of $$176$$, $$19$$ have a mass of $$177$$, $$27$$ have a mass of $$178$$, $$14$$ have a mass of $$179$$, and $$35$$ have a mass of a $$180$$ is$$178.55g$$

Note: The atomic number of the element is nothing but the number of electrons or number of protons. The mass number of the atom is nothing but the sum of number of protons and number of neutrons. Hafnium is one of the elements in the periodic table. The atomic number of hafnium is $$72$$. The symbol of hafnium is $$\text{Hf}$$. The mass number of hafnium is $$178.49$$.