Question

Average atomic weight of an element M is 51.7. If two isotopes of $M, M^{50}$ and $M^{52}$ are present, then percentage of occurrence of $M^{50}$ in nature will be.

• A. 85%
• B. 15%
• C. 50%
• D. 100%

Answer 1

Answer: (B)

15%

Answer 2

Given, Average atomic weight of element $(M) = 51.7$
Let's assume $M^{50}$ occurs with $x\%$.
Hence, $M^{52} = (100 - x)\%$
Average atomic weight
$51.7=\frac{x \times M^{50}+\left(100-x\right)\times M^{52}}{100}$
$51.7=\frac{x \times50+\left(100-x\right)52}{100}$
$5170 = 5200 - 2x$
$2x=5200-5170$
$x=15$
Hence, $\%$ of $M^{50}=15\%$