Three isotopes of an element have mass numbers, $M$ , $(M + 1)$ and $(M + 2)$ . If the mean mass number is $(M + 0.5)$ then which of the following ratios may be accepted for $M$ , $(M + 1)$ , $(M + 2)$ in that order?

1 : 1 : 1

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4 : 1 : 1

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3 : 2 : 1

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2 : 1 : 1

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Solution

The correct option is B $4 : 1 : 1$
Let a,b, c be the relative abundances of three isotopes having mass numbers M, (M+1) and (M+2) respectively.

$\frac{a M + b (M + 1) + c (M + 2)}{a + b + c} = M + 0.5$
$a M + b M + b + c M + 2 c = a M + b M + c M + 0.5 a + 0.5 b + 0.5 c$
$0.5 b + 1.5 c = 0.5 a$
$b + 3 c = a$
This is true for the option (B) $a : b : c = 4 : 1 : 1$

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Three isotopes of an element have mass numbers, M, (M+1) and (M+2). If the mean mass number is (M+0.5) then which of the following ratios may be accepted for M, (M+1), (M+2) in that order?

The correct option is B 4:1:1Let a,b, c be the relative abundances of three isotopes having mass numbers M, (M+1) and (M+2) respectively. aM+b(M+1)+c(M+2)a+b+c=M+0.5aM+bM+b+cM+2c=aM+bM+cM+0.5a+0.5b+0.5c0.5b+1.5c=0.5ab+3c=aThis is true for the option (B) a:b:c=4:1:1

Three isotopes of an element have mass numbers, $M$ , $(M + 1)$ and $(M + 2)$ . If the mean mass number is $(M + 0.5)$ then which of the following ratios may be accepted for $M$ , $(M + 1)$ , $(M + 2)$ in that order?