Question

An element has 2 isotopes . the mass of one isotopes is a-1 and the other is a+2. if the average is a , find the percentage of isotopes a-1 in the element

Answer 1

Answer:

66.67 %

Explanation:

Let us say the isotope of mass (a-1) has % abudance of (x) %

therefore % abudance of a+2 = (100-x)  %

thus,

x % of (a-1)  +  (100-x)% of a+2 = a

[x(a-1)] /100   +  [(100-x)(a+2)] / 100 = a

[ax-x] / 100  +  [100a + 200 -ax - 2x] / 100 = a

as the denominators are same

(ax-x) + (100 a + 200 -ax - 2x)     = a

             100

therefore,

100 a + 200 + ax - ax -x - 2x =  a X 100

- x - 2x = -200

- 3x = - 200

3x = 200

x = 200 / 3

x =  66.67 %

therefore isotope (a - 1)  has 66.67 % abudance

therefore isotope (a + 2) has (100-66.67) % abudance, i.e 33.33 %

therefore % of isotope (a - 1) is 66.67 %

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