The gold nucleus Au(198,79) undergoes alpha decay with a half-life of 2.70 days.
A. ) Find how many neutrons and protons are in the daughter nucleus produced by this decay.
B.) Find the activity in Bq (decays/sec) of a sample that contains 5.0 grams of Au(198,79) nuclei.
C.) A 2.5 kg suitcase at an airport absorbs 2.0 × 10−3 J/kg from 100 keV x-rays. How many photons are absorbed?
A) protons are 79-2 = 77
neutrons are (194-77)= 117
B) activity is dN/dt = -lamda*N
lamda is the decay constant = 0.693/T1/2 = 0.693/(2.7*24*60*60) =
2.97*10^-6 s^-1
N 5 grms
then dN/dt = -lamda*N
N is the no.of atoms = (5/198)6.02*10^23 = 1.52*10^22 nuclei
then activity dN/dt = -lamda*N = 2.97*10^-6*1.52*10^22 = 4.52*10^16
decays/sec
C) total energy absorbed is 2*2.5*10^-3 J
E= 5*10^-3 J
but E = n*h*f
h*f = 100*1000*1.6*10^-19 = 1.6*10^-14 J
no.of photons are n = E/(h*f) = (5*10^-3)/(1.6*10^-14) = 3.125*10^11 photons
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