Question:medium

Calculate the number of unit cell in \(0.5\) g metal if the product of volume and density of unit cell is \(6.65\times 10^{-23}\) g

Show Hint

Volume times density of a unit cell is the mass of one unit cell. Divide 0.5 g by this mass.
Updated On: Oct 1, 2026
  • \(6.340\times 10^{21}\)
  • \(7.518\times 10^{21}\)
  • \(5.625\times 10^{21}\)
  • \(8.492\times 10^{21}\)
Show Solution

The Correct Option is B

Solution and Explanation

Step 1: Reinterpret the given product:
$V\times d$ has units of cm$^3 \times$ g/cm$^3$ = g. It is the mass of a single cell, $6.65\times10^{-23}$ g.

Step 2: Count the cells:
Cells $= 0.5 \text{ g} / (6.65\times10^{-23} \text{ g per cell})$.
Write this as $\dfrac{5\times10^{-1}}{6.65\times10^{-23}} = 0.7519\times10^{22}$.
Moving the decimal point gives $7.518\times10^{21}$.

Step 3: Match:
Only option (B) agrees with this value. The mass of the sample is so much more than the mass of one cell that the count is of the order $10^{21}$.

Final Answer:
Number of unit cells $= 7.518\times10^{21}$, option (B). \[ \boxed{7.518\times10^{21} \text{ (B)}} \]
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