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mahoteacher
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Homework Statement
The masses of the following atoms are:
238 U → 238.050786(2)
234 Th→ 234.043598(5)
4 He → 4.002603
a) Calculate the energy available in the decay of 238U.
b) Calculate the decay rate of 238U
238U half time = 4.468*10^9yrs
c) If a block of uranium produces 1mW of power, how many disintegrations per second is this and what is the activity in Curies. Neglect other decays other than the one above.
d) Calculate the number of uranium atoms and the mass of the block.
- This is a question for an upper level medical physics class, but it seems to be relatively easy. So I am not sure if I am putting this in the right place.
Homework Equations
Mass calculation of radioactive decay
1 amu = 1.66 * 10^ -27 [kg]
t½ = ln2 / λ
A = λ*N = ΔN/ Δt
1 Ci = 3.7* 10^10 [s^-1]
The Attempt at a Solution
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a)
Δ amu = 238.050786(2) - 234.043598(5) - 4.002603 [amu] = 4.58*10^-3 [amu]
Δ mass = Δ amu * 1. 66*10^-27 [kg]
Δ mass = 4.58*10^-3 * 1.66 *10^-27 = 7.6106 *10^-30 [kg]
E = Δ mass * c^2
E = 7.6106 *10^-30 * 3*10^8 = 2.28 * 10^-21 J
b)
Δ t = 4.468*10^9 * 365 * 24 *60 * 60 = 1.409028* 10^17
Δ N = 6.022*10^23 atoms/ Δ amu = 7.9126* 10^-8
decay rate = ΔN/ Δt = 5.615 * 10^ -25
c)
disintegration per second = A = λN and 1 Ci = 3.7 * 10^10 [s^-1]
But how does power play a role? Does power affect the number of atoms? If yes how?
Assuming power has nothing to do with N, I am approaching the problem like this:
t½ = ln2/ λ
λ = 4.91932 * 10^ -18 [s^-1]
N = 6.022 * 10^ 23/ 238
A = λN = 12447 Bq = 3.36 * 10^ -7 [Ci]
d) since I don't know how power is related, I don't really know :(