Chapter 2 : Atomic structure and electronic configuration¶

Example 2.1 Page No : 32¶

In [1]:
import math

# Variables
Eg_k = 5.;                             #kinetic energy of alpha particles(in MeV)
Eg_K = 5.*(10**6)*1.6*(10**-19);       #kinetic energy of alpha particles(in J)
mv2 = 2.*Eg_K;
pi = 22./7;
phi = 180.;                            #firing angle
Z = 29.;                               #Atomic number

# Calculation
e = 1.6*(10**-19);			#electron charge(in C)
Eo = 8.85*10**-12;			#permittivity of free space
d = (Z*e**2/(2*pi*Eo*mv2))*(1+1)			#;

# Results
print 'distance of the closest approach alpha particles from the copper nucleus(in meter) = %.3e'%d

distance of the closest approach alpha particles from the copper nucleus(in meter) = 1.668e-14


Example 2.2 Page No : 33¶

In [2]:
import math

# Variables
e = 1.6*10**(-19);			#electron charge(in C)
m = 9.1*10**(-31);			#mass of electron(in Kg)
E_o = 8.854*10**(-12);			#permittivity of free space
h = 6.625*10**(-34);			#Planck constant
n = 1;			#Orbit number
Z = 1;			#atomic number
pi = 22./7;

# Calculation and Results
r_1 = (E_o*n**2*h**2)/(pi*m*Z**2*e**2);			#first orbit radius of hydrogen atom
print 'first orbit radius of hydrogen atom(in m) = %.4e'%r_1
Freq = m*(Z**2)*(e**4)/(4*(E_o**2)*(n**3)*h**3);			#
print 'Orbital frequency of electron(in Hz) = %.4e'%Freq

first orbit radius of hydrogen atom(in m) = 5.3077e-11
Orbital frequency of electron(in Hz) = 6.5407e+15


Example 2.3 Page No : 33¶

In [12]:

import math

# Variables
Z_1 = 1;			#atomic number for hydrogen
n_1 = 1;			#first orbit
r_1 = 0.529;			#radius of first orbit of electron for hydrogen
Z_2 = 2;			#atomic number for helium
n_2 = 2;			#second orbit

# Calculation
k = r_1*Z_1/n_1;
r_2 = k*((n_2)**2)/Z_2;			#radius of first orbit of electron for helium

# Results
print 'radius of the second bohr orbit in a math.singly ionized helium atom(in A) = ',r_2

radius of the second bohr orbit in a math.singly ionized helium atom(in A) =  1.058


Example 2.4 Page No : 33¶

In [18]:
import math

# Variables
n_1 = 1;			#first orbit
n_2 = 2;			#second orbit
n_3 = 3;			#third orbit

# Calculation
#E_1 = -13.6*(Z**2)/(1**2);
#E_2 = -13.6*(Z**2)/(2**2);
#E_3 = -13.6*(Z**2)/(3**2);
#E_3-E_1 = -13.6*(Z**2)*(-8/9);
#E_2-E_1 = -13.6*(Z**2)*(-3/4);
E_1 = -13.6/(1**2);			#energy of electron in the first bohr orbit of an atom
E_2 = -13.6/(2**2);			#energy of electron in the second bohr orbit of an atom
E_3 = -13.6/(3**2);			#energy of electron in the third bohr orbit of an atom

# Results
print 'ratio of energy released  = %.4f'%((E_3-E_1)/(E_2-E_1))

ratio of energy released  = 1.1852


Example 2.5 Page No : 34¶

In [1]:

import math

# Variables
m = 9.1*10**(-31);			#electron mass (in Kg)
Z = 1;			#atomic number
e = 1.6*10**(-19);			#electron charge(in C)
E_o = 8.25*10**(-12);			#permittivity of free space
n = 1;			#first bohr orbit

# Calculation
h = 6.63*10**(-34);			#planck consmath.tant
R_ps = m*(e**4)/(4*(E_o**2)*(h**3));			#number of revolutions per second

# Results
print 'revolutions per second of an electron in the bohr orbit of hydrogen atom = %.3e'%R_ps

# rounding off error

revolutions per second of an electron in the bohr orbit of hydrogen atom = 7.516e+15


Example 2.6 Page No : 35¶

In [3]:

import math

# Variables
n = 1.;			#first bohr orbit
Z = 1.;			#atomic number

# Calculation
m = 9.1*10**(-31);			#electron mass in Kg.
e = 1.6*10**(-19);			#electron charge(in C)
E_o = 8.85*10**(-12);			#permittivity of free space
h = 6.63*10**(-34);			#planck constant
v_n = m*(Z**2)*(e**4)/(4*(E_o**2)*(h**3)*(n**3));			#orbital frequency of an electron in the first bohr orbit in a hydrogen atom

# Results
print 'orbital frequency of an electron in the first bohr orbit in a hydrogen atom(in Hz) = %.3e'%v_n

# rounding off error

orbital frequency of an electron in the first bohr orbit in a hydrogen atom(in Hz) = 6.532e+15


Example 2.7 Page No : 35¶

In [2]:

import math

# Variables
m = 9.11*10**-31;			#mass of electron(in Kg)
Z = 1;          			#atomic number
n = 1;			            #first bohr orbit

# Calculation
E_o = 8.854*10**-12;			#permittivity of free space
h = 6.625*10**-34;			#planck consmath.tant
e = 1.6*10**-19;			#electron charge(in C)
E_k = (m*(Z**2)*(e**4))/(8*(E_o**2)*(n**2)*(h**2));			#Kinetic energy(in joule)
E = E_k/e;			#Kinetic energy(in eV)
E_t = -13.6*(Z**2/n**2);			#Total Energy(in eV)
E_p = E_t-E;			#Potential energy(in eV)

# Results
print 'Total energy in = %.1f eV'%E_t
print 'kinetic energy in = %.1f eV'%E
print 'potential energy in = %.1f eV'%E_p

Total energy in = -13.6 eV
kinetic energy in = 13.6 eV
potential energy in = -27.2 eV


Example 2.8 Page No : 35¶

In [4]:

import math

# Variables
h = 6.626*10**-34;			#planck consmath.tant
E_o = 8.825*10**-12;			#permittivity of free space
e = 1.6*10**-19;			#electron charge(in C)
n = 1;			#first bohr orbit
Z = 1;			#atomic number

# Calculation
v = Z*(e**2)/(2*E_o*n*h);			#velocity of electron in hydrogen atom in bohr first orbit

# Results
print 'velocity of electron in hydrogen atom in bohr first orbit(in meter/sec) = %.3e'%v

velocity of electron in hydrogen atom in bohr first orbit(in meter/sec) = 2.189e+06


Example 2.9 Page No : 35¶

In [10]:
import math

# Variables
n_1 = 1.;			#electron excited from ground state
h = 6.62*10**-34;			#Planck consmath.tant
c = 3.*10**8;			#speed of light
E_o = 8.825*10**-12;			#permittivity of free space
e = 1.6*10**-19;			#electron charge(in C)
m = 9.11*10**-31;			#mass of electron(in Kg)
E_1 = 10.2;			#energy excites the hydrogen from ground level(in eV)

# Calculation and Results
K = m*e**4/(8*(E_o**2)*(h**2))			#in joule
K_e = K/e;			#in eV
#E_1 = K_e*((1/n_1**2)-(1/n**2))
#1/(n**2) = 1/(n_1**2)-E_1/K_e
#n**2 = 1/(1/(n_1**2)-E_1/K_e)
n = (1/(1/(n_1**2)-E_1/K_e))**(1./2);			#principal quntum number when 10.2 eV energy excites electron
print 'principal quntum number when 10.2 eV energy excites electron = %.f'%(n)

W_1 = h*c/(E_1*e)*10**10;			#wavelength of radiation when 10.2 eV energy excites electron
print 'wavelength of radiation when 10.2 eV energy excites electron(in A) = %d'%W_1

E_2 = 12.09;			#energy excites the hydrogen from ground level(in eV)
n_2 = (1./(1./(n_1**2)-E_2/K_e))**(1./2);			#principal quntum number when 12.09 eV energy excites electron
W_2 = h*c/(E_2*e)*10**10;			#wavelength of radiation when 12.09 eV energy excites electron
print 'principal quntum number when 12.09 eV energy excites electron = %.f'%(n_2)
print 'wavelength of radiation when 12.09 eV energy excites electron in = %d A'%W_2

principal quntum number when 10.2 eV energy excites electron = 2
wavelength of radiation when 10.2 eV energy excites electron(in A) = 1216
principal quntum number when 12.09 eV energy excites electron = 3
wavelength of radiation when 12.09 eV energy excites electron in = 1026 A


Example 2.13 Page No : 58¶

In [8]:

import math

# Variables
At_w = 63.54;			#atomic weight of copper

# Calculation
W_a = At_w/N;			#weight of one atom(in gm)
W_p = W_a/63;			#weight of one proton(in gm)

# Results
print 'weight of one atom in %.3e gm'%W_a
print 'weight of one proton in %.3e gm'%W_p

weight of one atom in 1.055e-22 gm
weight of one proton in 1.675e-24 gm


Example 2.15 Page No : 59¶

In [10]:
import math

# Variables
Atw_Cu = 63.54;			#atomic weight of copper
Atw_Si = 28.09;			#atomic weight of silicon

# Calculation
# 5 atoms of copper working in Cu_5_Si
Tw_Cu = 5*Atw_Cu;			#total weight of copper used in copper silicide
Tw_Si = Atw_Si;			#total weight of silicon used in copper silicide
Percentage = (Tw_Si/(Tw_Cu+Tw_Si))*100;			#percentage of Si in Copper silicide

# Results
print 'percentage of Si in Copper silicide Cu_5_Si is = %.2f %%'%Percentage

percentage of Si in Copper silicide Cu_5_Si is = 8.12 %