Question

Thorium emits 4500 alpha particles per second per gram. One gram of thorium contains 2.61 x 1021 atoms.

Find the half-life of thorium.​

Answer 1

Given:

The no of alpha particles emitted per second = 4500

The mass of Thorium = 1 gm

The no of atoms in 1 g = 2.61 × 10²¹

To Find:

The half-life of thorium.​

Calculation:

- Thorium is emitting 4500 alpha particles per second.

⇒ The no of thorium atoms decaying per second = 4500

- After half-life period, the amount of thorium left = 1/2 = 0.5 gm

- No of atoms in 0.5 gm = 2.61 × 10²¹ × 0.5

⇒ N = 1.305 × 10²¹ atoms

- Half-life period = 1.305 × 10²¹/4500

⇒ T1/2 = 2.9 × 10¹⁷ s (or 4.833 × 10¹⁵ min)

- So, the half-life of thorium is 2.9 × 10¹⁷ s (or 4.833 × 10¹⁵ min).