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

Answer:

The activity is 811.77 Bq

Solution:

As per the question:

Half life of Thorium, $t_{\frac{1}{2}} = 1.405\times 10^{10}\ yrs$

Mass of Thorium, m = 200 mg = 0.2 g

M = 232 g/mol

Now,

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

$N = \frac{N_{o}m}{M}$

where

$N_{o }$ = Avagadro's number

Thus

$N = \frac{6.02\times 10^{23}\times 0.2}{232} = 5.19\times 10^{20}$

Also,

Activity is given by:

$\frac{0.693}{t_{\frac{1}{2}}}\times N$

$A= \frac{0.693}{1.405\times 10^{10}}\times 5.19\times 10^{20} = 2.56\times 10^{10}\ \yr$

$A = \frac{2.56\times 10^{10}}{365\times 24\times 60\times 60} = 811.77\ Bq$