Gas lanterns used on camping trips have mantles (small lacy bags that give off l

Question

Gas lanterns used on camping trips have mantles (small lacy bags that give off light) made from a rayon mesh impregnated with thorium and other materials. Thorium is used, even though it is radioactive, because it forms an oxide that can withstand being incandescent for long periods of time. Almost all natural thorium is 232Th90 which has a half life of 1.405x10^10 y.

(a) A typical mantle contains 271 mg of thorium. What is the reactivity of the mantle?


(b) If the half-life of thorium had been four times its actual value, by what factor would the activity of the mantle be changed?

Explanation / Answer

a) A=N

where =ln(2)/t1/2= ln(2)/(1.405E10*365.25*24*60*60)=1.56E-18

so we can use that 1 mole of Thorim= 232.038 g

so N=271E-3/232.038 * 6.022E23 =7.033E20

so A=1.56E-18*7.033E20=1097

b) if halflife went up by factor of four, goes down by a factor of 4 so activity goes down by a factor of 4

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