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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"`, m_{1} = 10.01294 u

Mass of boron isotope `""_5^11"B"`, m_{2} = 11.00931 u

Abundance of `""_5^10"B"`, η_{1} = x%

Abundance of `""_5^11"B"`, η_{2 }= (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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