Answer:
a) t = 27.00 h
b) B = 6.84 MeV/nucleon
Explanation:
a) The time can be calculated using the following equation:
<u>Where: </u>
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:
![t_{1/2} = \frac{ln(2)}{\lambda}](https://tex.z-dn.net/?f=%20t_%7B1%2F2%7D%20%3D%20%5Cfrac%7Bln%282%29%7D%7B%5Clambda%7D%20)
<u>Where:</u>
t(1/2): is the half life = 4.5 h
![\lambda = \frac{ln(2)}{t_{1/2}} = \frac{ln(2)}{4.5 h} = 0.154 h^{-1}](https://tex.z-dn.net/?f=%20%5Clambda%20%3D%20%5Cfrac%7Bln%282%29%7D%7Bt_%7B1%2F2%7D%7D%20%3D%20%5Cfrac%7Bln%282%29%7D%7B4.5%20h%7D%20%3D%200.154%20h%5E%7B-1%7D%20)
We have that the radiation measured is 64 times the maximum permissible level, thus R₀ = 64R:
b) The binding energy (B) can be calculated using the following equation:
![B = \frac{(Z*m_{p} + N*m_{n} - M_{A})}{A}*931.49 MeV/u](https://tex.z-dn.net/?f=B%20%3D%20%5Cfrac%7B%28Z%2Am_%7Bp%7D%20%2B%20N%2Am_%7Bn%7D%20-%20M_%7BA%7D%29%7D%7BA%7D%2A931.49%20MeV%2Fu)
<u>Where:</u>
Z: is the number of protons = 2 (for
)
: is the proton mass = 1.00730 u
N: is the number of neutrons = 2 (for
)
: is the neutron mass = 1.00869 u
: is the mass of the He atom = 4.002602 u
A = N + Z = 2 + 2 = 4
The binding energy of
is:
![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](https://tex.z-dn.net/?f=B%20%3D%20%5Cfrac%7B%282%2A1.00730%20%2B%202%2A1.00869%20-%204.002602%29%7D%7B4%7D%2A931.49%20MeV%2Fu%20%3D%207.35%5Ccdot%2010%5E%7B-3%7D%20u%2A931.49%20MeV%2Fu%20%3D%206.84%20MeV%2Fnucleon)
Hence, the binding energy per nucleon is 6.84 MeV.
I hope it helps you!