|Jul28-08, 07:15 PM||#1|
Radioactivity of Thorium
1. The problem statement, all variables and given/known data
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.)
Answer: 4.136E-5 hrs-1
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.?
2. Relevant equations
3. The attempt at a solution
N=(2.64E22 atoms)e^-(4.136E-5 hrs-1)(1hr)
mf=224.020186u + 4.002603u
m=228.022789u - 228.028715u
(5.52Mev)(1.602E-13J/Mev) = 8.843E-13 J
T=1468755.878 K = 1468482.878 C
Can someone help me catch my mistake? I'm not sure what I did wrong. Thank you.
|Jul28-08, 08:40 PM||#2|
One starts with No = 2.642E22 atoms, but how many atoms remain at the end of 1 hr? The difference No - N (1 hr) = the number of atoms that have decayed.
It's not that 10 g of Th-228 decayed, but a certain fraction of atoms in Th-228 have decayed, and that is related to the activity.
|Jul28-08, 09:02 PM||#3|
Thank you. I got it now.
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