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Question

# A student wants to have 3.011 × 1023 atoms each of magnesium and carbon elements. For this purpose, how much magnesium and carbon will he weigh in grams?

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Solution

## 12 g of carbon and 24.3 g of magnesium, each contains 6.022$×$1023 number of atoms. Now Let X g of carbon have 3.011$×$1023 number of atoms. Therefore, $\mathrm{X}=\frac{\mathrm{molar}\mathrm{mass}\mathrm{of}\mathrm{carbon}×\mathrm{number}\mathrm{of}\mathrm{atoms}\mathrm{of}\mathrm{carbon}}{\mathrm{Avogadro}\mathrm{number}}\phantom{\rule{0ex}{0ex}}\mathrm{X}=\frac{12×3.011×{10}^{23}}{6.022×{10}^{23}}\phantom{\rule{0ex}{0ex}}\mathrm{X}=6\mathrm{g}\mathrm{of}\mathrm{carbon}$ So, 6 g of carbon contains 3.011$×$1023 number of atoms. Again, Let X g of magnesium have 3.011$×$1023 number of atoms. Therefore, $\mathrm{X}=\frac{\mathrm{molar}\mathrm{mass}\mathrm{of}\mathrm{magnesium}×\mathrm{number}\mathrm{of}\mathrm{atoms}\mathrm{of}\mathrm{magnesium}}{\mathrm{Avogadro}\mathrm{number}}\phantom{\rule{0ex}{0ex}}\mathrm{X}=\frac{24×3.011×{10}^{23}}{6.022×{10}^{23}}\phantom{\rule{0ex}{0ex}}\mathrm{X}=12\mathrm{g}\mathrm{of}\mathrm{magnesium}$ So, 12 g of magnesium contains ​3.011$×$1023 number of atoms. Hence, he will weigh 12 g of magnesium and 6 g of carbon.

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