Question

Half-life of a substance is $20$ minutes, then the time between $33$ % decay and $67$ % decay will be:

• A. $20$ minute
• B. $40$ minute
• C. $50$ minute
• D. $10$ minute

Answer 1

The correct option is A $20$ minute

Suppose initial activity is 100. 33 % decay corresponds to the remaining activity of $100\times \frac{100-33}{100}=67$
Now $67$ % decay corresponds to the remaining activity of $100\times \frac{100-67}{100}=33$.
Thus for $33$% and $67$%, the activity reduces to one half from $67$ to $33$.
The time between $33$ % decay and $67$ % decay will be
a period equal to its half-life or $20$ minutes.