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  4. Average atomic weight of an element M is 51.7. If two isotopes of M, M50 and M52 are present, then percentage of occurrence of M50 in nature will be.

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Q. 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.

UPSEEUPSEE 2019

Solution:

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 $M^{50}=15\%$