Thorium (with half-life T1/2 = 1.913 yr. and atomic mass 228.028715 u) undergoes

Question

Thorium (with half-life T1/2 = 1.913 yr. and atomic mass 228.028715 u) undergoes alpha decay and produces radium (atomic mass 224.020186 u) as a daughter nucleus. (Assume the alpha particle has atomic mass 4.002603 u.)

(a) What is the decay constant of thorium? (Note that the answer must be in units of hrs-1.)

l = hrs-1 *
.000041 OK

(b) What percent of thorium is left after 200 days?

% *
81.99 OK

The energy released from the decay of 10 g of thorium is used to heat 3.8 kg of water (assume all the energy released goes into the water).
(c) What is the change in temperature of the water after 1 hr.?

DT =

Explanation / Answer

The reaction energy per reaction = (228.028715 - 224.020186 - 4.002603)*931.5MeV

= 5.520069MeV = 5.520069*1.60x10-13J/MeV = 8.832*10-13J per reaction.

Now in 10g of thorium there are N0 = (10/228.028715)*6.022x1023 = 2.641*1022 atom.

In 1hour there will be N = N0*(1 - e-t) reactions = 2.641*1022*(1-e-4.14x(10^-5)*1) = 1.0933*1018 reactions.

So the total energy released = 1.0933*1018*8.832*10-13 = 965609.71J released.

Now we have Q = 965609.71 = m*c*T

So T = 965609.71/(3.8*4186) = 60.704oC = 60.704 K

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