In [2]:

```
#initiation of variable
from math import exp
import math
from scipy import integrate
# calculating radial probability P= (4/ao^3)*integral(r^2 * e^(-2r/ao)) between the limits 0 and ao for r
#calculation
def integrand(x):
return ((x**2)*exp(-x))/2.0
Pr=integrate.quad(integrand,0,2,args=());#simplifying where as x=2*r/a0; hence the limits change between 0 to 2
#result
print "Hence the probability of finding the electron nearer to nucleus is",round(Pr[0],3);
```

In [4]:

```
#initiation of variable
from math import exp
import math
from scipy import integrate
# employing the formula for probability distribution similarly as done in Exa-7.2
#calculation
def integrand(x):
return (1.0/8)*((4.0*x**2)-(4.0*x**3)+(x**4))*exp(-x)
Pr1= integrate.quad(integrand,0,1,args=()) #x=r/ao; similrly limits between 0 and 1.
#result
print"The probability for l=0 electron is",round(Pr1[0],5)
#part2
def integrand(x):
return (1.0/24)*(x**4)*(exp(-x))
Pr2=integrate.quad(integrand,0,1); #x=r/ao; similarly limits between 0 and 1.
#result
print"The probability for l=1 electron is",round(Pr2[0],5)
```

In [6]:

```
#initiation of variable
from math import exp, sqrt
import math
from scipy import integrate
l=1.0; #given value of l
#calculation
am1=sqrt(l*(l+1)); #angular momentum==sqrt(l(l+1)) h
l=2.0 #given l
am2=sqrt(l*(l+1));
#result
print"The angular momenta are found out to be", round(am1,3)," h and",round(am2,3)," h respectively for l=1 and l=2.";
```

In [9]:

```
#initiation of variable
from math import sqrt
print "The possible values for m are [+2,-2] and hence any of the 5 components [-2h,2h] are possible for the L vector.";
print "Length of the vector as found out previously is %.2f*h.",round(sqrt(6),4);#angular momentum==sqrt(l(l+1)) h
```

In [11]:

```
#initiation of variable
uz=9.27*10**-24; t=1.4*10**3; x=3.5*10**-2; #various constants and given values
m=1.8*10**-25;v=750; # mass and velocity of the particle
#calculation
d=(uz*t*(x**2))/(m*(v**2)); #net separtion
#result
print"The distance of separation in mm is",round(d*10**3,3);
```

In [12]:

```
#initiation of variable
n1=1.0;n2=2.0;hc=1240.0; #hc=1240 eV.nm
E=(-13.6)*((1/n2**2)-(1/n1**2)); #Energy calculation
#calculation
w=hc/E; #wavelength
u=9.27*10**-24; B=2; #constants
delE= u*B/(1.6*10**-19); #change in energy
delw=((w**2/hc))*delE; #change in wavelength
#result
print"The change in wavelength in nm. is",round(delw,4);
```