Calculate the edge length of unit cell if metal having atomic radius 170 pm forms simple cubic unit cell.

Calculate the edge length of unit cell if metal having atomic radius 170 pm forms simple cubic unit cell.
  1. $1.17 \times 10^{-8} \mathrm{~cm}$
  2. $3.40 \times 10^{-8} \mathrm{~cm}$
  3. $5.12 \times 10^{-8} \mathrm{~cm}$
  4. $6.81 \times 10^{-8} \mathrm{~cm}$

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)

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