Half Life is the time taken for the radioactivity of an isotope to be halved.

**Example:**

Half life of substance X is 25 years.

If we take a 10 grams sample of X, then after 25 years, only 5 grams would remain.

Half life questions are fairly common in the BMAT exam. They may ask you questions which may look complicated but are actually simple.

Let us say you are given the half life of a substance and you are asked to find out the remaining amount after a certain amount of time. We use the following formula:

**Remaining mass of sample = Original mass of sample ÷ 2ⁿ**

Where ‘n’ is the number of half lives.

**Example:**

You have been given a 10 grams sample of isotope X. It’s half life is 4 minutes.

How many grams of the isotope will remain after 20 minutes?

Solution:

Half life = 4 minutes

Time given = 20 minutes

Number of half lives = 20 ÷ 4 = 5 half lives

Using the formula given,

Remaining mass = Original mass ÷ 2ⁿ (n is number of half lives)

Remaining mass = 10 ÷ 2⁵

Remaining mass = 10 ÷ 32

**Remaining mass = 0.3125 grams**

In the case where we have to find out the number of half lives when we are given original mass, remaining mass and the time.

**Example:**

400 g of a sample drops to 50 g after 300 days.

What is the half life of the sample?

Solution:

Initial mass = 400 g

Mass of sample after 1st half life = 200 g

Mass of sample after 2nd half life = 100 g

Mass of sample after 3rd half life = 50 g

The sample reached a mass of 50 g after 3 half lives.

3 half lives occurred in 300 days.

Time of one half life = 300 ÷ 3 = **100 days**