Answer :
The percentage of the isotope 50 (M-50) in nature can be determined by solving a weighted average mass equation, which results in 15%. Therefore, option B is the correct answer. The correct answer is(b).
To calculate the percentage of occurrence of isotope 50 (let's call it isotope M-50) in nature given the average atomic weight of an element M as 51.7, we can use the concept of weighted average mass of isotopes. Let x be the percentage of M-50 and (100-x) be the percentage of M-52 occurring in nature. The average atomic mass calculation would be:
(50 * x/100) + (52 * (100-x)/100) = 51.7
Solving for x gives us the percentage abundance of M-50 in nature. To solve this equation, multiply both sides by 100 to clear the denominator:
50x + 52(100 - x) = 5170
50x + 5200 - 52x = 5170
-2x = 5170 - 5200
-2x = -30
x = 15%
Thus, the naturally occurring percentage of M-50 is 15%, which corresponds to answer choice B. The correct answer is(b).
