In [1]:

```
from math import *
#Variable Declaration
V = 50; # Given potential difference, V
#Calculations
lamda = 12.24/sqrt(V); # Wavelength of the light, angstrom
#Result
print "The de-broglie wavelength of electron = %4.2f angstrom"%lamda
```

In [14]:

```
from math import *
#Variable Declaration
h = 6.62e-34; # Planck's constant, J-s
m0 = 1.6e-27; # Rest mass of proton, kg
c = 3.0e+8; # Speed of light, in m/s
v = c/20; # Velocity of the proton, in m/s
#Calculations
lamda = (h*sqrt(1-v**2/c**2))/(m0*v);
#Result
print "The de broglie wavelength associated with the proton = %4.2e m"%lamda
#answer differs due to rounding-off errors
```

In [16]:

```
#Variable Declaration
c = 3.0e+8; # Speed of light, m/s
v = 2.0e+8; # Velocity of the proton, m/s
m0 = 1.6e-27; # Rest mass of proton, kg
h = 6.62e-34; # Plancks constant,J-s
#Calculations
lamda = (h*sqrt(1-(v**2/c**2)))/(m0*v);
#Result
print "The wavelength of matter wave associated with the proton = %5.3e m"%lamda
#answer differs due to rounding-off errors
```

In [4]:

```
#Variable Declaration
a = 0.003; # Accuracy of the electron,in percent
s = 5e+03; # Speed of the electron,in m/s
del_v = (a/100)*s; # Change in velocity,in m/s
m0 = 9.1e-31; # Rest mass of the electron,in kg
hcut = 1.054e-34; # Plancks constant,J-s
#Calculations
del_x = hcut/(2*del_v*m0);
#Result
print "The uncertainity in the position of the electron = %4.2e m"%del_x
```

In [5]:

```
#Variable Declaration
del_t = 2.5e-14; # Lifetime of the hydrogen atom in excited state
hcut = 1.054e-34; # Planck's constant,in J-s
e = 1.6e-19; # Charge on electron,in C
#Calculations
del_E = hcut/(2*del_t*e); # Energy of the state, in eV
#Result
print "The minimum error in measurement of lifetime of excited state of hydrogen atom = %6.4f eV"%del_E
```

In [6]:

```
#Variable Declaration
del_x = 1e-09; # Uncertainty in position of the electron, m
m0 = 9.1e-031; # Rest mass of an electron, kg
hcut = 1.054e-034; # Planck's constant,in J-s
#Calculations
del_v = hcut/(2*del_x*m0); # Uncertainity in velocity of the electron
#Result
print "The uncertainity in the velocity of an electron = %4.2e m/s"%del_v
#Incorrect answer in the textbook
```

In [7]:

```
#Variable Declaration
hcut = 1.054e-34; # Reduced Planck's constant, Js
v = 3e+07; # Velocity of the electron, m/s
c = 3e+08; # Speed of light in vacuum, m/s
m0 = 9.1e-31; # Rest mass of an electron, kg
del_v = 3e+08; # Uncertainty in velocity of the electron, m/s
#Calculations
del_x = (hcut*sqrt(1-v**2/c**2))/(2*m0*del_v);
#Result
print "The smallest possible uncertainity in position of the electron = %6.4f angstrom"%(del_x/1e-010)
```

In [8]:

```
#Variable Declaration
n = 1;
m0 = 9.1e-031; # Mass of the electron, kg
a = 1e-10; # Width of the box, m
h = 6.63e-034; # Planck's constant, J-s
#Calculations
E = n**2*h**2/(8*m0*a**2);
#Result
print "The energy of the electron moving in 1D infinetly high potential box = %5.2e J"%E
```

In [25]:

```
#Variable Declaration
#n = [1,2]; # Shell numbers for two lowest permitted energy of the electron
m0 = 9.1e-31; # Mass of the electron, kg
a = 2.5e-10; # Width of the box, m
h = 6.63e-34; # Planck's constant, J-s
e = 1.6e-19; # Charge on electron, C
#Calculations&Results
E = round((h**2)/(8*m0*a**2*e));
for n in range(1,3):
print "The lowest two permitted energy values of an electron are"
print E*n**2,"eV"
```

In [10]:

```
#Variable Declaration
m0 = 1.67e-27; # Rest mass,in kg
a = 1e-14; # Size of the box
h = 6.63e-34; # Planck's constant,in J-s
n = 1; # Quantum number for lowest energy state
#Calculations
E_n = n**2*h**2/(8*m0*a**2);
#Result
print "The lowest energy of the neutron confined to the nucleus = %4.2e J"%E_n
```

In [11]:

```
#Variable Declaration
m0 = 9.1e-31; # Rest mass, kg
a = 1e-10; # Length of the box, m
h = 6.62e-34; # Planck's constat, J-s
n1 = 1; # Ground state
n2 = 2; # First excited state
e = 1.6e-19; # Charge on electron, C
#Calculations
E1 = (n1**2*h**2)/(8*m0*a**2*e);
E2 = (n2**2*h**2)/(8*m0*a**2*e);
del_E = E2-E1;
#Result
print "The energy difference between the ground state and the first excited state = %5.1f eV"%del_E
```