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Nuclei — Physics STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 SciencePhysicsNuclei3 Marks
Question
Boron has two stable isotopes, $^{10}_5\text{B }\text{ and }\ ^{11}_5\text{B}.$ 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 $^{10}_5\text{B }\text{ and }\ ^{11}_5\text{B}.$
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Answer

Mass of boron isotope $^{10}_5\text{B },\ \text{m}_1=10.01294\text{ u}$
Mass of boron isotope $^{11}_5\text{B },\ \text{m}_2=11.00931\text{ u}$
Abundance of $^{10}_5\text{B },\ \text{n}_1=\text{x}\%$
Abundance of $^{11}_5\text{B },\ \text{n}_2=(100-\text{x})\%$
Atomic mass of boron, m = 10.811 u
The atomic mass of boron atom is given as:
$\text{m}=\frac{\text{m}_1\text{n}_1+\text{m}_2\text{n}_2}{\text{n}_1+\text{n}_2}$
$10.811=\frac{10.01294\times\text{ x }+11.00931\times(100-\text{ x})}{\text{ x }+100-\text{ x}}$
1081.11 = 10.01294x + 1100.9312 - 11.00931x
$\therefore\ \text{x}=\frac{19.821}{0.99637}=19.89\%$
And 100 - X = 80.11%
Hence, the abundance of $^{10}_5\text{B is }19.89\%\text{ and that of }^{11}_5\text{B is }80.11\%.$

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