Chapter 7 - Atomic Physics

Example 1 - pg 217

In [1]:
#pg 217
#calculate the Radius, Velocity and Energy of electron
#Given :
import math
n =1.; # ground state
m = 9.109382*10**-31; #electron mass in kg
h = 6.625*10**-34; #planck's constant in Js
e = 1.602176*10**-19; # Charge of an electron in C
e0 = 8.854188*10**-12; # Vacuum permittivity in F/m
#calculations
r1 = (n**2*h**2*e0)/(math.pi*m*e**2);# Radius in A
v1 = e**2/(2*h*e0*n); # Velocity in m/s
E1 = -((m*e**4)/(8*n**2*h**2*e0**2)); # Energy of an electron in eV
# 1 A = 1.0*10**-10 m , 1 eV = 1.6*10**-19 J
#results
print"For hydrogen atom : \n Radius  =",round(r1*10**10,2),"A \n Velocity =",round(v1*10**-6,1),"x 10^6 m/s \n Energy of an electron (eV) = ",round(E1/(1.6*10**-19),1)

For hydrogen atom : 
 Radius  = 0.53 A 
 Velocity = 2.2 x 10^6 m/s 
 Energy of an electron (eV) =  -13.6

Example 2 - pg 218

In [2]:
#pg 218
#calculate the Rydberg constant
#Given :
#(a)
m = 9.109382*10**-31; #electron mass in kg
c = 2.997925*10**8; #Speed of light  in m/s
h = 6.626069*10**-34; #planck's constant in Js
e = 1.602176*10**-19; # Charge of an electron in C
e0 = 8.854188*10**-12; # Vacuum permittivity in F/m
#calculations
R = (m*e**4)/(8*h**3*e0**2*c);# Rydberg constant in m**-1
print"Rydberg constant for hydrogen (cm^-1) = ",round(R*10**-2,2)
#(b)
M = 1.672622*10**-27; # proton mass in kg
R1 = ((m*e**4)/(8*h**3*e0**2*c))*(1/(1 + (m/M))); # Rydberg Constant in m**-1
#1 m**-1 = 1.0*10**-2 cm**-1
#results
print"Rydberg Constant is (cm^-1) = ",round(R1*10**-2,2)

Rydberg constant for hydrogen (cm^-1) =  109737.16
Rydberg Constant is (cm^-1) =  109677.43

Example 3 - pg 219

In [4]:
#pg 219
#calculate the M/m value
#Given :
RH= 109677.58; #Rydberg constant for Hydrogen in cm**-1
RHe = 109722.269; #Rydberg constant for Helium in cm**-1
#calculations
#Ratio = M/m
Ratio = ((4*RH)- (RHe))/(4*(RHe-RH));
#results
print "M/m value is : ",round(Ratio,1)

M/m value is :  1840.4

Example 4 - pg 223

In [6]:
#pg 223
#calculate the Uncertainty in position
#Given
import math
h = 6.625*10**-34; #planck's constant in Js
m = 9.1*10**-31; #electron mass in kg
E1 = 13.6; #Energy of electron in eV
#1 eV = 1.6*10**-19 J
#calculations
p = math.sqrt(2*m*E1*1.6*10**-19); #momentum in kg m/s
deltax = h/(2*math.pi*p);
# 1 A = 1.0*10**-10 m
#results
print "Uncertainty in position (A) = ",round(deltax/(1.0*10**-10),2);

Uncertainty in position (A) =  0.53