Calculate the edge length of unit cell if metal having atomic radius 170 pm forms simple cubic unit cell.
- $1.17 \times 10^{-8} \mathrm{~cm}$
- $3.40 \times 10^{-8} \mathrm{~cm}$
- $5.12 \times 10^{-8} \mathrm{~cm}$
- $6.81 \times 10^{-8} \mathrm{~cm}$
Solution
In a simple cubic unit cell, atoms are located at the corners and contact each other along the cube edges.
This implies the edge length $a$ is equal to twice the atomic radius: $a = 2r$.
Given $r = 170 \text{ pm}$, convert to centimeters using $1 \text{ pm} = 10^{-10} \text{ cm}$:
$r = 170 \times 10^{-10} \text{ cm} = 1.70 \times 10^{-8} \text{ cm}$.
Substitute into the relation:
$a = 2 \times 1.70 \times 10^{-8} = 3.40 \times 10^{-8} \text{ cm}$.
This value corresponds to option B.
Asked in: MHT CET 2025 (05 May Shift 2)