MHT CET · Chemistry · Solid State
An element with BCC structure has edge length of \(500 \mathrm{pm}\). If its density is \(4 \mathrm{~g} \mathrm{~cm}^3\), find atomic mass of the element?
- A \(150 \mathrm{~g} \mathrm{~mol}^{-1}\)
- B \(100 \mathrm{~g} \mathrm{~mol}^{-1}\)
- C \(125 \mathrm{~g} \mathrm{~mol}^{-1}\)
- D \(250 \mathrm{~g} \mathrm{~mol}^{-1}\)
Answer & Solution
Correct Answer
(A) \(150 \mathrm{~g} \mathrm{~mol}^{-1}\)
Step-by-step Solution
Detailed explanation
\(\mathrm{a}=500 \mathrm{pm}=500 \times 10^{-10} \mathrm{~cm} \)
\( =5 \times 10^{-8} \mathrm{~cm} \)
\( \mathrm{Z}=2(\text { for } \mathrm{BCC}) \)
\( \mathrm{d}=\frac{\mathrm{ZM}}{\mathrm{N}_{\mathrm{A}} \cdot \mathrm{a}^3} \)
\( \mathrm{M}=\frac{\mathrm{d} \times \mathrm{N}_{\mathrm{A}} \times \mathrm{a}^3}{\mathrm{Z}}=\) \(\frac{4 \times 6.022 \times 10^{23} \times\left(5 \times 10^{-8}\right)^3}{2} \)
\( \mathrm{M}=150 \mathrm{~g} \mathrm{~mol}^{-1}\)
\( =5 \times 10^{-8} \mathrm{~cm} \)
\( \mathrm{Z}=2(\text { for } \mathrm{BCC}) \)
\( \mathrm{d}=\frac{\mathrm{ZM}}{\mathrm{N}_{\mathrm{A}} \cdot \mathrm{a}^3} \)
\( \mathrm{M}=\frac{\mathrm{d} \times \mathrm{N}_{\mathrm{A}} \times \mathrm{a}^3}{\mathrm{Z}}=\) \(\frac{4 \times 6.022 \times 10^{23} \times\left(5 \times 10^{-8}\right)^3}{2} \)
\( \mathrm{M}=150 \mathrm{~g} \mathrm{~mol}^{-1}\)
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