Answer:
a) t = 27.00 h
b) B = 6.84 MeV/nucleon
Explanation:
a) The time can be calculated using the following equation:
[tex] R = R_{0}e^{-\lambda*t} [/tex]
Where:
R: is the radiation measured at time t
R₀: is the initial radiation
λ: is the decay constant
t: is the time
The decay constant can be calculated as follows:
[tex] t_{1/2} = \frac{ln(2)}{\lambda} [/tex]
Where:
t(1/2): is the half life = 4.5 h
[tex] \lambda = \frac{ln(2)}{t_{1/2}} = \frac{ln(2)}{4.5 h} = 0.154 h^{-1} [/tex]
We have that the radiation measured is 64 times the maximum permissible level, thus R₀ = 64R:
[tex] \frac{R}{64R} = e^{-\lambda*t} [/tex]
[tex] t = -\frac{ln(1/64)}{\lambda} = -\frac{ln(1/64)}{0.154 h^{-1}} = 27.00 h [/tex]
b) The binding energy (B) can be calculated using the following equation:
[tex]B = \frac{(Z*m_{p} + N*m_{n} - M_{A})}{A}*931.49 MeV/u[/tex]
Where:
Z: is the number of protons = 2 (for [tex]^{4}_{2}He[/tex])
[tex]m_{p}[/tex]: is the proton mass = 1.00730 u
N: is the number of neutrons = 2 (for [tex]^{4}_{2}He[/tex])
[tex]m_{n}[/tex]: is the neutron mass = 1.00869 u
[tex]M_{A}[/tex]: is the mass of the He atom = 4.002602 u
A = N + Z = 2 + 2 = 4
The binding energy of [tex]^{4}_{2}He[/tex] is:
[tex]B = \frac{(2*1.00730 + 2*1.00869 - 4.002602)}{4}*931.49 MeV/u = 7.35\cdot 10^{-3} u*931.49 MeV/u = 6.84 MeV/nucleon[/tex]
Hence, the binding energy per nucleon is 6.84 MeV.
I hope it helps you!
