Q5 / 150 · MHT CET 2025 (5 May Shift 2) · Chemistry

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

  • A
    $1.17 \times 10^{-8} \mathrm{~cm}$
  • Correct answer
    B
    $3.40 \times 10^{-8} \mathrm{~cm}$
  • C
    $5.12 \times 10^{-8} \mathrm{~cm}$
  • D
    $6.81 \times 10^{-8} \mathrm{~cm}$

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.

Hence, the correct answer is option: 'B'.

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