Question

Boron has two isotopes ${{\text{B}}^{10}}$ and ${{\text{B}}^{11}}$. The average atomic mass of Boron is $10.2$. Find relative % of each isotope.

Answer 1

Isotopes are atoms of the same element with the same atomic number and different mass number. All isotopes of the same element have the same number of protons but different number of neutrons.
Formula Used:
Average atomic mass =\dfrac{\text{mass }\\!\\!%\\!\\!\text{ of isotope 1+ mass }\\!\\!%\\!\\!\text{ of isotope 2+}.....\text{+ mass }\\!\\!%\\!\\!\text{ of isotope n}}{\text{n}}

Complete step by step answer:
Let the amount of ${{\text{B}}^{10}}$ be {\text{x% }} and thus, the amount of ${{\text{B}}^{11}}$ will be $\left( {{\text{100}} - {\text{x}}} \right)\%$
According to the formula, Average atomic mass =$\dfrac{{\left( {10 \times {\text{x}}} \right) + \left( {100 - {\text{x}}} \right)11}}{{100}} = 10.8$
$\Rightarrow 10{\text{x}} + 1100 - 11{\text{x}} = 1080$
Solving for x, we get:
$\Rightarrow {\text{x}} = 1100 - 1080 = 20\%$
Therefore, $\left( {{\text{100}} - {\text{x}}} \right)\% = \left( {100 - 20} \right){\text{ }}\% = 80{\text{ }}\%$
Thus, the amount of ${{\text{B}}^{10}} = 20\%$ and ${{\text{B}}^{11}} = 80\%$ in the given isotope.

Note:
-The total number of neutrons and protons present in an atom is called the mass number of the atom. The mass calculated by summing up the element’s masses, each multiplied by its natural abundance on Earth is called the “average atomic mass”.
-Atoms of the different elements with the same mass number by different atomic numbers are called “Isobars”.
-Isodiaphers are a set of atoms for which the difference in the number of protons and neutrons are the same.
-Isotones are a set of nuclides with the same number of neutrons.
The discovery of isotopes was due to the study of radioactivity and was first observed in case of radioactive elements.
-Isotopes will be stable, that is, they will not be radioactive only if their, $\dfrac{\text{n}}{\text{p}}>0.5$, where n is the number of neutrons and p is the number of protons. Most atoms have isotopes, but they are either not present in abundance or are radioactive with a very short half-life.