The average atomic mass of a sample of element X is 16.2 u. What are the percentages of isotopes¹⁶₈X and¹⁸₈X in the sample?

Academic Chemistry NCERT Class 9

Atomic number: The atomic number of an element is equal to the number of protons in the nucleus of its atom. e.g., Oxygen has 6 protons hence atomic no. = 6.

Mass number: The mass number of an atom is equal to the number of protons and neutrons in its nucleus.

Nucleons = number of protons + number of neutrons Example: Protons + Neutrons = Nucleus = Mass number 6 + 6 = 12

Isotopes: Isotopes are atoms of the same element which have different mass numbers but the same atomic numbers

E.g., 11H, 21H,31H

Now, to find out the percentage of each in the sample:

Let the percentage of ¹⁶₈X be x and the percentage of ¹⁸₈X be 100 – x.

Therefore

$\frac{16x}{100}+\frac{18(100-x)}{100}=16.2$

$\frac{16x}{100}+\frac{1800-18x}{100}=16.2$

$\frac{16x- 1800+18x}{100}=16.2$

$ -2x +1800 = 16.2 \times 100$

$-2x = 1620 - 1800$

$-2x = -180$

$x= \frac{180}{2}=90$

Therefore, ¹⁶₆X = 90% and ¹⁸₈X =10%.

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Updated on: 15-Mar-2023

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