#importing modules
import math
from __future__ import division
#Variable declaration
r0=1.2; #radius(fm)
A=7; #mass number
#Calculation
r=r0*A**(1/3); #radius of Li(fm)
#Result
print "The radius of Li is",round(r,4),"fm"
#importing modules
import math
from __future__ import division
#Variable declaration
M=235.043945; #atomic mass of uranium(u)
Z=92; #atomic number of uranium
mp=1.007825; #mass of proton(kg)
N=143; #no.of neutrons
mn=1.008665; #mass of neutron(kg)
A=235; #number of nucleons
#Calculation
B=(((Z*mp)+(N*mn)-(M))/A)*931.5; #Binding energy(MeV)
#Result
print "The binding energy per nucleon is",round(B,3),"MeV"
#importing modules
import math
from __future__ import division
#Variable declaration
#After removing one neutron from Ca(A=43;Z=20) it becomes Ca(A=42;Z=20)
M=41.958622; #mass of Ca(A=42;Z=20)(kg)
mn=1.008665; #mass of neutron(kg)
E=42.95877; #mass of Ca(A=43;Z=20)(kg)
#Calculation
C=M+mn;
D=C-E;
B=D*931.5; #Binding energy of neutron(MeV)
#Result
print "The binding energy of neutron is",round(B,4),"MeV"
#importing modules
import math
from __future__ import division
#Variable declaration
mBe=9.012182; #Atomic mass of beryllium(u)
mHe=4.002603; #Atomic mass of helium
mn=1.008665; #mass of neutron(kg)
mC=12.000000; #Atomic mass of carbon
#Calculation
Q=(mBe+mHe-mn-mC)*931.5 #energy balance of the reaction(MeV)
#Result
print "The Q-value is",round(Q,1),"MeV"
#importing modules
import math
from __future__ import division
#Variable declaration
mLi=7.016004; #mass of Lithium(A=7)(u)
mH=1.007825; #mass of Hydrogen(A=1)(u)
mHe=4.002603; #mass of helium(A=4)(u)
p=0.5; #energy of proton(MeV)
#Calculation
Q=(mLi+mH-2*(mHe))*931.5 #energy balance of the reaction(MeV)
#The energy of 2 alpha particles is equal to the Q-value + energy of proton.
Ealpha=(Q+p)/2; #energy of each alpha particle(MeV)
#Result
print "The Q-value of the reaction is",round(Q,2),"MeV"
print "The energy of each alpha particle is",round(Ealpha,3),"MeV"
print "answer for energy in the book varies due to rounding off errors"
#importing modules
import math
from __future__ import division
#Variable declaration
wt=1000; #weight(gm)
A=235; #mass number of uranium
N=(6.02*10**23/A)*wt; #no.of nuclei in 1kg of uranium
Q=208; #energy-balance of the reaction
#Calculation
E=N*Q; #Energy released(MeV)
#1MeV=4.45*10^-20kWh
E=E*4.45*10**-20;
#Result
print "The energy released is",round(E/10**7,3),"*10**7 kWh"
#importing modules
import math
from __future__ import division
#Variable declaration
wt=5000; #weight(gm)
A=235; #mass number of uranium
Ef=208; #Energy released per fission(MeV)
#Calculation
N=(6.02*10**23/A)*wt; #number of nuclei in 5 Kg
E=N*Ef; #Energy(MeV)
E=E*1.6*10**-13; #Energy(J)
T=24*60*60; #time
P=E/T; #power(MW)
#Result
print "The power output of a nuclear reactor is",round(P/10**6),"MW"
print "answer given in the book is wrong"
#importing modules
import math
from __future__ import division
#Variable declaration
A=235; #mass number of uranium
p=1000; #amount of electric power produced(MW)
e=0.32; #energy conversion efficiency of the plant
f=200; #fission energy per event(MeV)
#Calculation
I=p/e; #Input nuclear energy(MW)
TE=I*(10**6)*3600*24*365; #total energy(J)
EF=f*(10**6)*1.6*10**-19; #Energy released per fission event(J)
N=TE/EF; #Number of nuclei required
M=N*A/(6.02*10**23); #corresponding mass(g)
#Result
print "The amount of uranium required is",round(M*10**-3,1),"kg"
print "answer in the book varies due to rounding off errors"
#importing modules
import math
from __future__ import division
#Variable declaration
q=1.6*10**-19; #charge of the particle(c)
B=1; #magnetic field(T)
m=1.67*10**-27; #mass of proton(kg)
r=0.5; #radius(m)
#Calculation
omega=(q*B)/m; #angular frequency(radian/s)
v=(omega/(2*math.pi))*10**-8; #frequency(MHz)
s=omega*r; #speed of proton(m/s)
K=(m*(s**2))*(1/2)*6.27*10**12; #kinetic energy of protons emerging from cyclotron(MeV)
#Result
print "The frequency of oscillator to accelerate protons is",round(omega/10**8,2),"*10**8 radian/s"
print "The speed of proton is",round(s/10**7,1),"*10**7 m/s"
print "The kinetic energy of protons emerging from the cyclotron is",int(K),"MeV"
#importing modules
import math
from __future__ import division
#Variable declaration
rho=1.83*10**17; #average density of carbon nucleus(kg/m^3)
m=12; #mass(u)
e=1.66*10**-27;
#Calculation
r=(m*e/((4/3)*math.pi*rho))**(1/3)*10**15; #radius(fm)
#Result
print "The radius is",round(r,2),"fm"
#importing modules
import math
from __future__ import division
#Variable declaration
q=1.6*10**-19; #charge of the particle(c)
B=5; #magnetic field(T)
m=9.1*10**-31; #mass of electron(kg)
#Calculation
v=(q*B)/(2*math.pi*m); #cyclotron frequency(Hz)
#Result
print "cyclotron frequency of electron is",round(v/10**11,1),"*10**11 Hz"
#importing modules
import math
from __future__ import division
#Variable declaration
k=1.5; #maximum kinetic energy(MeV)
m=1.67*10**-27; #mass of proton(kg)
q=1.6*10**-19; #charge of particle(c)
r=0.35; #radius(m)
#Calculation
B=math.sqrt(k*10**6*q*2*m)/(q*r); #magnetic field(T)
#Result
print "The mgnetic field is",round(B,1),"T"
#importing modules
import math
from __future__ import division
#Variable declaration
m=1.67*10**-27; #mass of proton(kg)
q=1.6*10**-19; #charge of particle(q)
v=25; #cyclotron frequency(MHz)
#Calculation
B=(v*10**6*2*math.pi*m)/q; #magnetic field(T)
#Result
print "The required magnetic field is",round(B,4),"T"
#importing modules
import math
from __future__ import division
#Variable declaration
v=20; #cyclotron frequency(MHz)
B=1.3; #magnetic field(T)
#Calculation
d=2*math.pi*v*10**6/B; #charge to mass ratio of proton(C/kg)
#Result
print "charge to mass ratio of proton is",round(d/10**6,2),"*10**6 C/kg"