Question

Mantles for gas lanterns contain thorium, because it forms an oxide that can survive being heated to incandescence for long periods of time. Natural thorium is almost 100% 232Th, with a half-life of 1.405 ✕ 1010 y. If an average lantern mantle contains 200 mg of thorium, what is its activity (in Bq)?

Answer 1

The activity is 811.77 Bq

Solution:

As per the question:

Half life of Thorium,
`t_{(1)/(2)} = 1.405* 10^(10)\ yrs`

Mass of Thorium, m = 200 mg = 0.2 g

M = 232 g/mol

Now,

No. of nuclei of Thorium in 200 mg of Thorium:

`N = (N_(o)m)/(M)`

where

`N_(o )` = Avagadro's number

Thus

`N = (6.02* 10^(23)* 0.2)/(232) = 5.19* 10^(20)`

Also,

Activity is given by:

`\frac{0.693}{t_{(1)/(2)}}* N`

`A= (0.693)/(1.405* 10^(10))* 5.19* 10^(20) = 2.56* 10^(10)\ \yr`

`A = (2.56* 10^(10))/(365* 24* 60* 60) = 811.77\ Bq`