In [4]:

```
#importing modules
import math
from __future__ import division
#Variable declaration
h=6.63*10**-34; #plancks constant(J sec)
m=9.11*10**-31; #mass(kg)
a=10**-10; #width of box(m)
e=1.602*10**-19; #charge(coulomb)
#Calculations
E1=(h**2)/(8*m*e*a**2); #least energy(eV)
#Result
print "least energy is",round(E1,2),"eV"
print "answer given in the book is wrong"
```

In [5]:

```
#importing modules
import math
from __future__ import division
#Variable declaration
delta_x=5*10**-10; #interval(m)
a=25*10**-10; #width(m)
#Calculations
P=2*delta_x/a; #probability of finding the particle
#Result
print "probability of finding the particle is",P
```

In [11]:

```
#importing modules
import math
from __future__ import division
from scipy.integrate import quad
#Variable declaration
a=1; #assume
#Calculations
def zintg(x):
return (2/a)*(1/2)*(1-math.cos(2*math.pi*x/a))
P1=quad(zintg,0.45,0.55)[0]
#Result
print "probability of finding the particle is",round(P1*100,2),"%"
```

In [14]:

```
#importing modules
import math
from __future__ import division
#Variable declaration
h=6.63*10**-34; #planks constant(Js)
m=9.1*10**-31; #mass(kg)
a=2.5*10**-10; #width(m)
e=1.6*10**-19; #charge(coulomb)
n1=1;
n2=2;
n3=3; #energy states
#Calculations
E1=n1**2*(h**2)/(8*m*e*a**2); #least energy(eV)
E2=n2**2*E1; #energy in 2nd excited state(eV)
E3=n3**2*E1; #energy in 3rd excited state(eV)
delta_E=E2-E1; #difference of energy between 2nd and 1st excited states(eV)
#Result
print "least energy is",int(E1),"eV"
print "energy in 2nd excited state is",int(E2),"eV"
print "energy in 3rd excited state is",int(E3),"eV"
print "difference of energy between 2nd and 1st excited states is",int(delta_E),"eV"
```

In [23]:

```
#importing modules
import math
from __future__ import division
#Variable declaration
h=6.63*10**-34; #planks constant(Js)
m=9.1*10**-31; #mass(kg)
a=10; #width(angstrom)
e=1.6*10**-19; #charge(coulomb)
n1=1;
n2=2;
n3=3; #energy states
#Calculations
lamda1=2*a/n1; #de-Broglie wavelength of first energy state(angstrom)
lamda2=2*a/n2; #de-Broglie wavelength of second energy state(angstrom)
lamda3=2*a/n3; #de-Broglie wavelength of third energy state(angstrom)
E1=n1**2*(h**2)/(8*m*e*(a*10**-10)**2); #energy in 1st excited state(eV)
E2=n2**2*E1; #energy in 2nd excited state(eV)
E3=n3**2*E1; #energy in 3rd excited state(eV)
#Result
print "de-Broglie wavelength of first three energy states are",int(lamda1),"angstrom",int(lamda2),"angstrom",round(lamda3,2),"angstrom"
print "energies of first three energy states are",round(E1,2),"eV",round(E2,4),"eV",round(E3,3),"eV"
print "answer in the book varies due to rounding off errors"
```

In [33]:

```
#importing modules
import math
from __future__ import division
#Variable declaration
h=6.63*10**-34; #planks constant(Js)
a=0.2*10**-9; #width(m)
e=1.602*10**-19; #charge(coulomb)
n5=5; #energy state
E5=230*e; #energy 0f 5th state(J)
En=10**3*e; #energy(eV)
#Calculations
E1=E5/n5**2; #energy in 1st excited state(eV)
m=h**2/(8*E1*a**2); #mass(kg)
n=math.sqrt(En/E1); #quantum state
#Result
print "energy in 1st excited state is",round(E1*10**19,1),"*10**-19 J"
print "mass is",round(m*10**31,1),"*10**-31 kg"
print "quantum state is",round(n,1)
print "as n is not an integer, En is not permitted value of energy"
```

In [48]:

```
#importing modules
import math
from __future__ import division
#Variable declaration
e=1.6*10**-19; #charge(coulomb)
E1=0.04*e; #energy(J)
V=0.03*e; #energy barrier(J)
E2=0.025*e; #energy(J)
E3=0.03*e; #energy(J)
m=1; #assume
k1=1; #assume
#Calculations
x=math.sqrt(E1-V);
y=math.sqrt(E1+V);
R1=((math.sqrt(E1)-x)/(math.sqrt(E1)+y))**2; #reflection coefficient
T1=1-R; #transmission coefficient
k2=math.sqrt(2*m*(E3-V));
R2=((k1-k2)/(k1+k2))**2; #reflection coefficient
T2=4*k1*k2/(k1+k2)**2; #transmission coefficient
#Result
print "reflection coefficient in 1st case is",round(R1,2)
print "answer given in the book is wrong"
print "transmission coefficient in 1st case is",round(T1,2)
print "for E=0.025, E<V. so transmission coefficient is 0 and reflection coefficient is 1"
print "reflection coefficient in 3rd case is",int(R2)
print "transmission coefficient in 3rd case is",int(T2)
```

In [54]:

```
#importing modules
import math
from __future__ import division
#Variable declaration
T=0.5; #transmission coefficient
a=1;
b=6;
c=1;
#Calculations
k1byk2=(b+math.sqrt((b**2)-(4*a*c)))/(2*a);
x=k1byk2**2;
EbyV=x/(x-1); #value of E/V
#Result
print "value of E/V is",round(EbyV,2)
```

In [40]:

```
#importing modules
import math
from __future__ import division
#Variable declaration
m=9.1*10**-31; #mass(kg)
a1=5*10**-10; #width(m)
a2=10*10**-10; #width(m)
e=1.6*10**-19; #charge(coulomb)
V0=5; #energy barrier(eV)
E1=1; #energy of electron(eV)
E2=2;
chi=1.054*10**-34; #plancks constant(Js)
#Calculations
beta1=math.sqrt(2*m*(V0-E1)*e/chi**2); #value of beta(m-1)
x1=int(-2*a1*beta1);
beta2=math.sqrt(2*m*(V0-E2)*e/chi**2); #value of beta(m-1)
x2=round(-2*a1*beta2,1);
T1=math.exp(x1); #transmission probability in 1st case
T2=math.exp(x2); #transmission probability in 1st case
x3=int(-2*a2*beta1);
x4=round(-2*a2*beta1,1);
T1dash=math.exp(x3); #transmission probability in 2nd case
T2dash=math.exp(x4); #transmission probability in 1st case
#Result
print "transmission probabilities in 1st case are",round(T1*10**5,1),"*10**-5 and",round(T2*10**4,1),"*10**-4"
print "transmission probabilities in 2nd case are",round(T1dash*10**9,1),"*10**-9 and",round(T2dash*10**9,2),"*10**-9"
print "answer for transmission probability in 2nd case given in the book is wrong"
```

In [59]:

```
#importing modules
import math
from __future__ import division
#Variable declaration
m=9.1*10**-31; #mass(kg)
a=10**-10; #width(m)
e=1.6*10**-19; #charge(coulomb)
V0=5; #energy barrier(eV)
E=2.5; #energy of electron(eV)
chi=1.05*10**-34; #plancks constant(Js)
#Calculations
x=16*E*(V0-E)/V0**2;
y=-2*a*math.sqrt(2*m*(V0-E)*e/chi**2);
#T=x*math.exp(y); #transmission coefficient
#Result
print "transmission coefficient is",int(x),"math.exp (",round(y,3),")"
```

In [76]:

```
#importing modules
import math
from __future__ import division
#Variable declaration
P=10**21; #probability(T per sec)
m=4*1.6*10**-27; #mass(kg)
a=2*10**-14; #width(m)
e=1.67*10**-19; #charge(coulomb)
V0=30; #energy barrier(eV)
E=4.2; #energy of electron(eV)
chi=1.05*10**-34; #plancks constant(Js)
#Calculations
x=P*16*E*(V0-E)/V0**2;
y=-2*a*math.sqrt(2*m*(V0-E)*10**6*e/chi**2);
T=x*math.exp(y); #transmission coefficient
tow=1/T; #average lifetime of nucleus(years)
#Result
print "average lifetime of nucleus is",round(tow/10**17,1),"*10**17 years"
print "answer given in the book is wrong"
```