3: The Atomic Structure

Example number 3.1, Page number 25

In [4]:
#import modules
import math
from __future__ import division

#Variable declaration
Z=79;         #atomic number of gold
e=1.6*10**-19;       #electron charge(C)
Eo=8.854*10**-12;     #absolute permitivity of free space(F/m)
K=7.68*1.6*10**-13;    #kinectic energy(J)

#calculation
D=(2*Z*e**2)/(4*math.pi*Eo*K);        #closest distance of approach(m)

#Result
print "The closest distance of approach is",round(D/1e-14,2),"*10**-14 m"

The closest distance of approach is 2.96 *10**-14 m

Example number 3.2, Page number 28

In [18]:
#import modules
import math
from __future__ import division

#Variable declaration
Z=1;       #atomic number of hydrogen
e=1.6*10**-19;    #electron charge(C)
h=6.625*10**-34;    #plank's constant(J-s)
m=9.1*10**-31;      #mass of an electron(kg)
Eo=8.854*10**-12;        #absolute permitivity of free space(F/m)
c=3*10**8;               #speed of light(m/s)
n=1;                 #ground state

#calculation
v=9*10**9*(2*math.pi*Z*e**2)/(n*h);         #velocity of ground state(m/s)
r=(Eo*n**2*h**2)/(math.pi*m*e**2);          #radius of Bohr orbit in ground state(m)
t=(2*math.pi*r)/v;        #time taken by electron to traverse the bohr first orbit(s)
R=(m*(e**4))/(8*(Eo**2)*(h**3)*c);       #Rhydberg contstant(m^-1)
#v=v*10**-5;
#v=math.ceil(v*10**3)/10**3;   #rounding off to 3 decimals
#r=r*10**10;
#R=R/10**6;

#Result
print "velocity of ground state",round(v/1e+5,2),"*10^5 m/s"
print "radius of Bohr orbit in ground state",round(r/1e-10,2),"*10^-10 m"
print "time taken by electron to traverse the bohr first orbit",round(t/1e-16,2),"micro s"
print "Rhydberg constant is",round(R/1e+6,3),"*10**6 m^-1"
print "answer for Rhydberg contstant given in the book differs in the 2nd decimal point"

velocity of ground state 21.85 *10^5 m/s
radius of Bohr orbit in ground state 0.53 *10^-10 m
time taken by electron to traverse the bohr first orbit 1.53 micro s
Rhydberg constant is 10.901 *10**6 m^-1
answer for Rhydberg contstant given in the book differs in the 2nd decimal point

Example number 3.3, Page number 29

In [35]:
#import modules
import math
from __future__ import division

#Variable declaration
B=2.179*10**-16;      #constant(J)
h=6.6*10**-34;      #plank's constant(J-s)

#calculation
E3=-B/3**2;       #energy in 3rd orbit(J)
E2=-B/2**2;       #energy in 2nd orbit(J)  
f=(E3-E2)/h;      #frequency of radiation(Hz) 

#Result
print "frequency of radiation",round(f/1e+16,1),"*10**16 Hz"

frequency of radiation 4.6 *10**16 Hz

Example number 3.4, Page number 29

In [38]:
#import modules
import math
from __future__ import division

#Variable declaration
Z=1;     #atomic number of hydrogen
e=1.6*10**-19;       #electron charge(C)
h=6.625*10**-34;     #plank's constant(J-s)
m=9.1*10**-31;       #mass of an electron(kg)
Eo=8.854*10**-12;    #absolute permitivity of free space(F/m)
n=1;         #ground state

#Calculation
f=(m*Z**2*e**4)/(4*Eo**2*h**3);         #frequency(Hz)

#Result
print "the frequency is",round(f/1e+15,2),"*10**15 Hz"

the frequency is 6.54 *10**15 Hz

Example number 3.5, Page number 30

In [24]:
#import modules
import math
from __future__ import division

#Variable declaration
Z=1;
n=1;
e=1.6*10**-19;    #the charge on electron(C)
h=6.62*10**-34;   #Plank's constant
Eo=8.854*10**-12;     #absolute permitivity of free space(F/m)
m=9.1*10**-31;     #mass of electron(kg)

#calculation
v=Z*(e**2)/(2*Eo*n*h);        #velocity(m/s)
E=-m*(Z**2)*(e**4)/(8*(Eo*n*h)**2);      #energy of hydrogen atom(J)
f=m*(Z**2)*(e**4)/(4*(Eo**2)*(n*h)**3);        #frequecy(Hz)

#Result
print "velocity is",round(v*10**-6,2),"*10**6 m/s"
print "energy of hydrogen atom",round(E*10**19,1),"*10**-19 J"
print "frequecy",round(f/1e+15,1),"*10**15 Hz"
print "answer for velocity given in the book is wrong"
print "answer for frequency given in the book varies due to rounding off errors"

velocity is 2.18 *10**6 m/s
energy of hydrogen atom -21.7 *10**-19 J
frequecy 6.6 *10**15 Hz
answer for velocity given in the book is wrong
answer for frequency given in the book varies due to rounding off errors

Example number 3.8, Page number 38

In [58]:
#import modules
import math
from __future__ import division

#Variable declaration
h=6.625*10**-34;     #Plank's constant
c=3*10**8;          #speed of light(m/s)
E1=10.2;           #energy(eV)
E2=12.09;           #energy(eV)
e=1.6*10**-19;        #the charge on electron(C)

#calcualtion
#principal quantum numbers are 2 & 3 respectively
lamda1=c*h/(E1*e)*10**10;       #wavelength for E1(angstrom)
lamda2=c*h/(E2*e)*10**10;       #wavelength for E2(angstrom)

#Result
print "wavelength for 10.2 eV is",int(lamda1),"angstrom"
print "wavelength for 12.09 eV is",int(lamda2),"angstrom"
print "answers given in the book differ due to rounding off errors"

wavelength for 10.2 eV is 1217 angstrom
wavelength for 12.09 eV is 1027 angstrom
answers given in the book differ due to rounding off errors

Example number 3.9, Page number 39

In [62]:
#import modules
import math
from __future__ import division

#Variable declaration
R=10967700;      #Rydberg constant(m^-1)

#calculation
long_lamda=4/(3*R);     #as n1=1 and n2=2
long_lamda=long_lamda*10**10;           #long wavelength(angstrom)
short_lamda=1/R;         #as n1=1 and n2=infinity
short_lamda=short_lamda*10**10;         #long wavelength(angstrom)

#Result
print "Long wavelength is",round(long_lamda),"angstrom"
print "Short wavelength is",round(short_lamda),"angstrom"

Long wavelength is 1216.0 angstrom
Short wavelength is 912.0 angstrom