In [1]:

```
import math
#Variable declaration
e = 1.6e-019; # Energy equivalent of 1 eV, J
h = 6.62e-034; # Planck's constant, Js
c = 3.00e+008; # Speed of light in vacuum, m/s
h_bar = h/(2*math.pi); # Reduced Planck's constant, Js
R_N = 1e-015; # Range of nuclear force, m
#Calculations
# As delta_E*delta_t = h_bar/2 and delta_E = m_pion*c^2, solving for m_pion
m_pion = h_bar*c/(2*R_N*e*1e+006); # Mass of the meson, MeV/c^2
#Result
print "The estimated mass of meson from Heisenberg uncertainty principle = %.2f MeV/c^2"%(m_pion)
```

In [2]:

```
import math
#Variable declaration
e = 1.6e-019; # Energy equivalent of 1 eV, J
h = 6.62e-034; # Planck's constant, Js
c = 3.00e+008; # For simplicity assume speed of light to be unity
h_bar = h/(2*math.pi); # Reduced Planck's constant, Js
m_W = 80.4; # Energy equivalent of mass of W- particle, MeV
#Calculations
R_W = h_bar*c/(2*m_W*e*1e+009); # Range of W- particle, m
delta_t = h_bar/(2*m_W*e*1e+009); # Time during which the energy conservation is violated, s
#Results
print "The range of W- particle = %3.1e m"%R_W
print "The time during which the energy conservation is violated = %1.0e s"%delta_t
```

In [3]:

```
import math
#Variable declaration
m_p = 0.938; # Rest mass energy of the proton, GeV
K = 6.4; # Kinetic energy of the proton projectile, GeV
#Calculations
E_cm = math.sqrt(2*m_p**2+2*m_p*K); # Centre of mass energy of proton collsion with the fixed proton target, GeV
Q = 2*m_p - 4*m_p; # Q value of the reaction, GeV
K_th = -3*Q; # Threshold kinetic energy required to produce the antiprotons, GeV
K = 1000; # Kinetic energy of the protons in Tevatron, GeV
E_cm_T = math.sqrt(2*m_p**2+2*m_p*K); # Centre-of-mass energy available for the reaction for the Tevatron, GeV
#Results
print "The available energy in the center on mass = %4.2f GeV"%E_cm
print "The threshold kinetic energy required to produce the antiprotons = %3.1f GeV"%K_th
print "The centre-of-mass energy available for the reaction for the Tevatron = %d GeV"%E_cm_T
```

In [4]:

```
import math
#Variable declaration
m_p = 0.938; # Rest mass energy of the proton, GeV
E_cm = 14000; # Centre of mass energy of colliding proton beams at LHC, GeV
#Calculations
# As E_cm = math.sqrt(2*m_p**2+2*m_p*K), solving for K
K = E_cm**2*1e+009/(2*m_p); # Approx. kinetic energy of the protons needed for fixed-target experiment, eV
#Result
print "The kinetic energy of the protons needed for fixed-target experiment = %3.1e eV"%K
```