#importing modules
import math
from __future__ import division
#Variable declaration
N0=1; #assume
#Calculation
f=(N0/2)/N0; #fraction after t1/2
f1=(N0/4)/N0; #fraction after 2 half lives
f2=(N0/(2**5))/N0; #fraction after 5 half lives
f3=(N0/(2**10))/N0; #fraction after 10 half lives
#Result
print "fraction after 2 half lives is",f1
print "fraction after 5 half lives is",f2
print "fraction after 10 half lives is",f3
#importing modules
import math
from __future__ import division
#Variable declaration
thalf=2.7*24*60*60; #half life(s)
m=1*10**-6; #mass(gm)
Na=6.02*10**23; #avagadro number(atoms/mol)
M=198; #molar mass(g/mol)
t=8*24*60*60;
#Calculation
lamda=0.693/thalf; #decay constant(per sec)
N=m*Na/M; #number of nuclei(atoms)
A0=lamda*N; #activity(disintegrations per sec)
A=A0*math.exp(-lamda*t); #activity for 8 days(decays per sec)
#Result
print "decay constant is",round(lamda*10**6,2),"*10**-6 per sec"
print "activity is",round(A0/10**9,2),"*10**9 disintegrations per sec"
print "activity for 8 days is",round(A/10**9,2),"*10**9 decays per sec"
#importing modules
import math
from __future__ import division
#Variable declaration
thalf=5570*365*24*60*60; #half life(s)
dNbydt=3.7*10**10*2*10**-3; #number of decays per sec
m=14;
Na=6.02*10**23; #avagadro number(atoms/mol)
#Calculation
lamda=0.693/thalf; #decay constant(per sec)
N=dNbydt/lamda; #number of atoms
mN=m*N/Na; #mass of 2mCi(g)
#Result
print "mass of 2mCi is",round(mN*10**4,2),"*10**-4 g"
#importing modules
import math
from __future__ import division
#Variable declaration
thalf=1.25*10**9; #half life(yr)
r=10.2; #ratio of number of atoms
#Calculation
a=1+r;
lamda=0.693/thalf; #decay constant(per yr)
t=math.log(a)/lamda; #time(yr)
#Result
print "the rock is",round(t/10**9,2),"*10**9 yrs old"
#importing modules
import math
from __future__ import division
#Variable declaration
mU=232.037131; #atomic mass of U(u)
mHe=4.002603; #atomic mass of He(u)
E=931.5; #energy(MeV)
KE=5.32; #kinetic energy of alpha particle(MeV)
#Calculation
mTh=mU-mHe-(KE/E); #atomic mass of Th(u)
#Result
print "atomic mass of Th is",round(mTh,5),"u"
#importing modules
import math
from __future__ import division
#Variable declaration
E=931.5; #energy(MeV)
mX=11.011433; #mass of 11C(u)
mXdash=11.009305; #mass of 11B(u)
me=0.511;
#Calculation
Q=(E*(mX-mXdash))-(2*me); #Q value for decay(MeV)
#Result
print "maximum energy is",round(Q,2),"MeV.minimum energy is zero"
#importing modules
import math
from __future__ import division
#Variable declaration
mK=39.963999; #mass of K(u)
mAr=39.962384; #mass of Ar(u)
E=931.5; #energy(MeV)
#Calculation
Q=(mK-mAr)*E; #kinetic energy of neutrino(MeV)
#Result
print "kinetic energy of neutrino is",round(Q,3),"MeV"
#importing modules
import math
from __future__ import division
#Variable declaration
mN=12.018613; #mass of N(u)
mC=12; #mass of C(u)
me=0.000549; #mass of me(u)
E=931.5; #energy(MeV)
Egamma=4.43; #energy of emitted gamma ray(MeV)
#Calculation
Q=(mN-mC-(2*me))*E; #Q value(MeV)
Emax=Q-Egamma; #maximum kinetic energy(MeV)
#Result
print "maximum kinetic energy is",round(Emax,2),"MeV"