#Variable declaration
m=9.1*10**-31 #mass of electron (kg)
h=6.6*10**-34 #planck's constant (joule-second)
e=1.6*10**-19 #charge of electron (coulomb)
#Calculation
from sympy import *
V=Symbol('V')
a=(h*10**10)/(2.0*m*e*V)**(1/2.0) #wavelength of electron = h/(2*m*e*v)**(1/2) (Å)
#Result
print"\n Wavelength of electron accelerated through a potential difference V =",a,"Å"
#Variable declaration
m_e=9.1*10**-31 #mass of electron (kg)
m=100*10**-3 #mass of object (kg)
v=1000 #velocity of electron and object (meter/second)
h=6.63*10**-34 #planck's constant (joule-second)
#Calculation
#(i) de Broglie wavelength of electron
lembda_e=h/(m_e*v) #de Broglie wavelength of electron
#(ii) de Broglie wavelength of object
lembda=h/(m*v) #de Broglie wavelength of object
#Result
print"\n(i) de Broglie wavelength of electron =",round(lembda_e*10**10),"A"
print"(ii) de Broglie wavelength of object =%.2e"%lembda,"m"
print"Note: In the book the answer of part(ii) is wrong"
#Variable declaration
e=1.6*10**-19 #charge of electron (coulomb)
T=100*e #kinetic energy (joule)
m_e=9.1*10**-31 #mass of electron (kg)
m_p=1.67*10**-27 #mass of proton (kg)
m_alpha=4*m_p #mass of alpha particle (kg)
h=6.63*10**-34 #planck's constant (joule-second)
#Calculation
lembda_e=(h*10**10)/(2*m_e*T)**(1.0/2.0) #de Broglie wavelength of electron (Å)
lembda_p=(h*10**10)/(2*m_p*T)**(1.0/2.0) #de Broglie wavelength of proton (Å)
lembda_alpha=(h*10**10)/(2*m_alpha*T)**(1.0/2.0) #de Broglie wavelength of alpha particle (Å)
#Result
print"De Broglie wavelength of electron =",round(lembda_e,2),"Å"
print"De Broglie wavelength of proton =",round(lembda_p,3),"Å"
print"De Broglie wavelength of alpha particle =",round(lembda_alpha,3),"Å"
#Variable declaration
h=6.63*10**-34 #planck's constant (joule-second)
m=9.1*10**-31 #mass of electron (kg)
lembda=5896*10**-10 #wavelength of yellow spectral line of sodium (meter)
e=1.6*10**-19 #charge of electron (coulomb)
#Calculation
T_j=h**2/(2*m*lembda**2) #kinetic energy of the electron (joule)
T_eV=T_j/e #kinetic energy of the electron (eV)
#Result
print"Kinetic energy of electron =%.2e"%T_j,"J =%.1e"%T_eV,"eV"
#Variable declaration
h=6.63*10**-34 #planck's constant (joule-second)
m_n=1.67*10**-27 #mass of neutron (kg)
T=300 #Temperature (kelvin)
k=1.38*10**-23 #Boltzmann constant (joule/kelvin)
#Calculation
E=(3*k*T)/2.0 #Kinetic energy of thermal neutron (joule)
lembda=(h*10**10)/(2*m_n*E)**(1/2.0) #Wavelength of thermal neutron (Å)
#Result
print"The wavelength of thermal neutron =%.3g"%lembda,"Å"
#Variable declaration
h=6.63*10**-34 #planck's constant (joule-second)
m_H2=2*1.67*10**-27 #mass of hydrogen molecule (kg)
T=27+273 #room temperature (kelvin)
k=1.38*10**-23 #Boltzmann constant (joule/kelvin)
#Calculation
lembda=(h*10**10)/(2*m_H2*k*T)**(1/2.0) #de Broglie wavelength of hydrogen molecule (Å)
#Result
print"The de Broglie wavelength of hydrogen molecules at their most probable speed =%.2f"%lembda,"Å"
#Variable declaration
a=0.51 #Value of m0*c**2 (Mev)
#Calculation
import math
T=a*(math.sqrt(2.0)-1) #Kinetic energy (MeV)
print"Kinetic energy of electron =",round(T,2),"MeV"
#Variable declaration
a=0.51 #Value of m0*c**2 (MeV)
b=0.0124 #Value of h*c (MeV Å)
lembda_X=0.1 #Short wavelength limit of continuous X-ray spectrum (Å)
#Calculation
lembda=lembda_X/(1+(2*a*lembda_X)/b)**(1/2.0) #de Broglie wavelength of relativistic electrons
print"De Broglie wavelength of relativistic electrons =",round(lembda,3),"Å"
#Variable declaration
r=0.53 #Radius of the first Bohr orbit in hydrogen atom (Å)
#Calculation
import math
lembda=2*math.pi*r #de Broglie wavelength of electron in first Bohr orbit in hydrogen atom
#Result
print"\nde Broglie wavelength of electron in first Bohr orbit in hydrogen atom =%.1f"%lembda,"Å"
#Variable declaration
v=10000 #speed of object (meter/second)
accu_v=0.0001 #accuracy of speed of object
m_b=0.05 #mass of the bullet (kg)
h=1.054*10**-34 #planck's constant (joule-second)
m_e=9.1*10**-31 #mass of electron (kg)
#Calculation
#(a) fundamental accuracy of position for bullet
p_b=m_b*v #momentum of bullet (kg m/s)
p_uncer_b=p_b*accu_v #uncertainty in momentum of bullet (kg m/s)
x_uncer_b=h/p_uncer_b #minimum uncertainty in position of bullet (meter)
#(b) fundamental accuracy of position for electron
p_e=m_e*v #momentum of electron (kg m/s)
p_uncer_e=p_e*accu_v #uncertainty in momentum of electron (kg m/s)
x_uncer_e=h/p_uncer_e #uncertainty in position of electron (meter)
print"\n(a) Minimum uncertainty in position of bullet =%.1e"%x_uncer_b,"meter"
print"(b) uncertainty in position of electron =%.3g"%x_uncer_e,"meter"
print"Note:The answers given in the book are wrong. \nAlso in the solution they have used speed=1000 while in the question it is given to be equal to 10000."
#Variable declaration
h=1.054*10**-34 #planck's constant (joule-second)
m=9.1*10**-31 #mass of electron (kg)
x_uncer=1*10**-10 #uncertainty in the position of elctrons (meter)
e=1.6*10**-19 #charge of electron (coulomb)
#Calculation
#(i) uncertainty in the momentum of electron
p_uncer=h/x_uncer #The uncertainty in the momentum of electron (kg m/s)
#(ii) kinetic energy of electron
T=p_uncer**2/(2*m*e) #kinetic energy of electron (eV)
#Result
print"\n(i) The uncertainty in the momentum of electron =",p_uncer,"kg m/s"
print"(ii) Kinetic energy of electron =%.1f"%T,"eV"
#Variable declaration
h=1.054*10**-34 #planck's constant (joule-second)
x=10**-14 #dimension of the nucleus (meter)
c=3*10**8 #speed of light (meter/second)
e=1.6*10**-19 #charge of electron (coulomb)
#Calculation
#(i) Uncertainty in the momentum of electron
p_uncer=h/x #The uncertainty in the momentum of electron (kg m/s)
#(ii) kinetic energy of electron
T=(p_uncer*c)/(e*10**6) #kinetic energy of electron (MeV)
#Result
print"\n(i) The uncertainty in the momentum of electron =",p_uncer,"kg m/s"
print"(ii) Kinetic energy of electron =",round(T)," MeV"
#Variable declaration
h=1.054*10**-34 #planck's constant (joule-second)
x=10**-14 #dimension of the nucleus (meter)
e=1.6*10**-19 #charge of electron (coulomb)
m=1.67*10**-27 #mass of proton (kg)
#Calculation
#(i) Uncertainty in the momentum of electron
p_uncer=h/x #The uncertainty in the momentum of electron (kg m/s)
#(ii) kinetic energy of proton
T=(p_uncer**2)/(2*m*e*10**6) #kinetic energy of proton (MeV)
#Result
print"\n(i) The uncertainty in the momentum of electron =",p_uncer,"kg m/s"
print"(ii) Kinetic energy of proton =",round(T,2),"MeV (approx)"
#Variable declaration
h=1.054*10**-34 #planck's constant (joule-second)
delta_t=10**-12 #time for which nucleus remains in excited state (second)
#Calculation
delta_E=h/delta_t #uncertainty in the energy of the gamma ray photon (joule)
#Result
print"\nThe uncertainty in the energy of the gamma ray photon =",delta_E,"J"
#Variable declaration
delta_t=10**-8 #life-time of the average excited atom (second)
#Calculation
delta_f=1/delta_t #minimum uncertainty in the frequency of photon (radian/second)
#Result
print"\nminimum uncertainty in the frequency of photon =%.g"%delta_f,"rad/s"
#Variable declaration
h=1.054*10**-34 #planck's constant (joule-second)
e=1.6*10**-19 #charge of electron (coulomb)
m=9.1*10**-31 #mass of electron (kg)
E0=8.8542*10**-12 #permittivity of free space (C**2/N*m**2)
#Calculation
#(i) radius of ground state of hydrogen atom
r=(4*math.pi*E0*h**2)/(m*e**2) #radius of ground state of hydrogen atom (meter)
#(ii) Binding energy of electron in hydrogen atom in the ground state
E=(-0.5*m*e**4)/(4*math.pi*E0*h)**2 #binding energy of electron in hydrogen atom in the ground state (joule)
#Result
print"\n(i) Radius of ground state of hydrogen atom =%.1e"%r,"m (in scientific notation) OR 0.53*10**-10"
print"(ii) Binding energy of electron in ground state of hydrogen atom =%.2e"%E,"J"