# Chapter 7:Many electron Atoms¶

## Example 7.1,Page no:230¶

In [2]:
#Variable declaration
r= 5*(10**(-17))  #radius of spherical electron, m
Me= 9.1*(10**(-31))  #mass of electron, kg
h= 6.63*(10**(-34))  #Planck's constant, J.s

#Calculation
import math
hbar= h/(2*(math.pi))  #reduced Planck's constant, J.s
v= (5*math.sqrt(3)/4)*(hbar/(Me*r))  #using Eqn 7.1, Page 230
c= 3*(10**8)  #velocity of light, m/s
v= v/c  #converting in terms of c, m/s

#Result
print"The velocity of electron in times of c is:%.3g"%v,"c"

The velocity of electron in times of c is:1.67e+04 c


## Example 7.2,Page no:241¶

In [3]:
#Variable declaration
n= 2  #outer (2s) orbit of lithium
E2= -5.39  #Ionisation energy of lithium, for n=2 eV
E1= -13.6  #for n=1, eV

#Calculation
Z= n*(math.sqrt(E2/E1)) #modification factor for effective charge
e= 1.6*(10**(-19))  #charge of an electron, C
Ceffective = Z*e

#Result
print"The effective charge is: ",round(Ceffective/e,2),"e or%.3g"%Ceffective,"C"


The effective charge is:  1.26 e or2.01e-19 C


## Example 7.3,Page no:248¶

In [4]:
#Variable declaration
n= 2  #for 2p state
Ao= 5.29*(10**(-11))  #Bohr's orbit for n=1, m
f= 8.4*(10**14)  #frequency of revolution, Hz ,using Eqn 4.4

#Calculation
Mo= 4*(math.pi)*(10**(-7))  #Magnetic constant, T.m/A
e= 1.6*(10**(-19))  #charge of an electron, C
B= (Mo*f*e)/(2*r)  #Magnetic field, T
Mb= 9.27*(10**(-24))  #Bohr Magneton, J/T
Um= Mb*B  #Magnetic energy, J
Um= Um/e  #converting to eV

#Result
print"The magnetic energy for electron  is:%.2g"%Um,"eV"
print"\nThe energy difference is twice this,which is:%.2g"%(2*Um),"eV"

The magnetic energy for electron  is:2.3e-05 eV

The energy difference is twice this,which is:4.6e-05 eV


## Example 7.8,Page no:257¶

In [5]:
#Variable declaration
l= 0.180  #wavelength, nm
l= l* 10**(-9)  #converting to m
c= 3*(10**8)  #velocity of light, m/s

#Calculation
f= c/l  #frequency, Hz
R= 1.097*(10**7)  #Rydberg's constant, per m
Z= 1+(math.sqrt((4*f)/(3*c*R)))  #using Eqn 7.21

#Result
print"The element has atomic number: ",round(Z)

The element has atomic number:  27.0