Question

Find the volume occupied by a particle in a simple cubic unit cell if the radius of a particle in it is 190 pm.

• A. \(6.410\times 10^{-23} \text{cm}^3\)
• B. \(3.625\times 10^{-23} \text{cm}^3\)
• C. \(5.715\times 10^{-23} \text{cm}^3\)
• D. \(2.873\times 10^{-23} \text{cm}^3\)

Hint:

Volume of one sphere is \(\frac43\pi r^3\), with \(r = 190\) pm \(=1.9\times10^{-8}\) cm.

Answer 1

The Correct Option is D

Step 1: Per-cell count
Simple cubic has $8\times\frac18 = 1$ particle per cell, so the occupied volume equals one sphere.

Step 2: Calculate
$V = \frac{4\pi}{3}(190\times10^{-10})^3$ cm$^3$. With $190^3 = 6.859\times10^{6}$ and $10^{-30}$, the cube is $6.859\times10^{-24}$.
Multiplying by 4.189 gives $2.873\times10^{-23}$ cm$^3$, option (D).

Final Answer:
One particle occupies $2.873\times10^{-23}$ cm$^3$, option (D). \[ \boxed{2.873\times10^{-23}\ \text{cm}^3} \]