Question

The half life of Cs-137 is 30.2 years. If the initial mass of the sample is 1.00kg, how much will remain after 151 years? Round to the nearest hundredth.

Answer 1

`\huge\boxed{\sf 0.03\ kg}`

Step-by-step explanation:

Half Life of Ca-137 = 30.2 years

Time duration = 151 years

Initial mass = 1 kg

Number of half lives:

To find the number of half lives, we will divide the actual time duration by the half life of Cs.

So,

= Time duration/half life

= 151/30.2

= 5 half lives

This means, 5 half lives have passed.

Half life:

• The time in which half of the original quantity is decayed and half is left.

So, the amount of Cs after:

1 half life:

= 1/2

= 0.5 kg

2 half lives:

= 0.5/2

= 0.25 kg

3 half lives:

= 0.25/2

= 0.125 kg

4 half lives:

= 0.125/2

= 0.0625 kg

5 half lives:

= 0.0625/2

= 0.03 kg

`\rule[225]{225}{2}`