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Question
Boron has two stable isotopes, `""_5^10"B"` and `""_5^11"B"`. Their respective masses are 10.01294 u and 11.00931 u, and the atomic mass of boron is 10.811 u. Find the abundances of `""_5^10"B"` and `""_5^11"B"`.
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Solution
Mass of boron isotope `""_5^10"B"`, m1 = 10.01294 u
Mass of boron isotope `""_5^11"B"`, m2 = 11.00931 u
Abundance of `""_5^10"B"`, η1 = x%
Abundance of `""_5^11"B"`, η2 = (100 − x)%
Atomic mass of boron, m = 10.811 u
The atomic mass of boron atom is given as:
`"m" = ("m"_1η_1 + "m"_2η_2)/(η_1 + η_2)`
`10.811 = (10.01294 xx "x" + 11.00931 xx (100 -"x"))/("x" + 100 - "x")`
1081.11 = 10.01294 x + 1100.931 − 11.00931 x
∴ x = `(19.821)/0.99637`
= 19.89%
And 100 − x = 80.11%
Hence, the abundance of `""_5^10"B"` is 19.89% and that of `""_5^11"B"` is 80.11%.
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