In [2]:

```
#initiation of variable
from math import sqrt
#The solution is purely theoretical and involves a lot of approximations.
print"The value of shift in frequency was found out to be delf=7.14*fo*10^-7*sqrt(T) for a star composing of hydrogen atoms at a temperature T.";
T=6000.0; #temperature for sun
delf=7.14*10**-7*sqrt(T);#change in frequency
#result
print"The value of frequency shift for sun(at 6000 deg. temperature) comprsing of hydrogen atoms is",delf," times the frequency of the light."
```

In [2]:

```
#initiation of variable
from math import sqrt,pi, exp, log
kT=0.0252;E=10.2 # at room temperature, kT=0.0252 standard value and given value of E
#calculation
n2=2;n1=1; g2=2*(n2**2);g1=2*(n1**2); #values for ground and excited states
t=(g2/g1)*exp(-E/kT); #fraction of atoms
#result
print"The number of hydrogen atoms required is %.1e" %(1.0/t)," which weighs %.0e" %((1/t)*(1.67*10**-27)),"Kg"
#partb
t=0.1/0.9;k=8.65*10**-5 #fracion of atoms in case-2 is given
T=-E/(log(t/(g2/g1))*k); #temperature
#result
print"The value of temperature at which 1/10 atoms are in excited state in K is %.1e" %round(T,3);
```

In [8]:

```
#initiation of variable
from math import log
#theoretical part a
print'The energy of interaction with magnetic field is given by uB and the degeneracy of the states are +-1/2 which are identical.\nThe ratio is therefore pE2/pE1 which gives e^(-2*u*B/k*T)';
#partb
uB=5.79*10**-4; #for a typical atom
t=1.1;k=8.65*10**-5; #ratio and constant k
#calculation
T=2*uB/(log(t)*k); #temperature
#result
print"The value of temperature ar which the given ratio exists in K is",round(T,3);
```

In [12]:

```
#initiation of variable
from math import pi
p=0.971; A=6.023*10**23; m=23.0; # various given values and constants
#calculation
c= (p*A/m)*10**6; # atoms per unit volume
hc=1240.0; mc2=0.511*10**6; # hc=1240 eV.nm
E= ((hc**2)/(2*mc2))*(((3/(8*pi))*c)**(2.0/3)); #value of fermi energy
#result
print"The fermi energy for sodium is",round(E*10**-18,4),"eV";#multiply by 10^-18 to convert metres^2 term to nm^2
```