## Example 7.2.1, Page 308¶

In [1]:
#Variable declaration
E_p = 30.; # Energy required for one pair, eV
n = 150000; # Number of pairs

#Calculations
E_a = n*E_p/10**6; # Energy of alpha particle, Mev

#Result
print "The energy of alpha particle  : %3.1f Mev"%E_a

The energy of alpha particle  : 4.5 Mev


## Example 7.3.1, Page 308¶

In [2]:
#Variable declaration
E = 5.48e+06; # Energy of alpha particle, eV
C = 50e-012; # Capacitance of the chamber, F
R = 10**6; # Resistance, ohm
E_p = 35; # Energy required to produced an ion pair, eV

#Calculations
n = E/E_p; # Number of ion pair produced
e = 1.6e-019; # Charge of an electron, C
V =( n*e)/C; # Pulse height, V
I = V/R; # current produced, A

#Results
print "The pulse height  =  %4.3e V \n Current produced  = %5.3e A"%(V,I)

The pulse height  =  5.010e-04 V
Current produced  = 5.010e-10 A


## Example 7.3.2, Page 309¶

In [3]:
#Variable declaration
E_p = 35.; # Energy required to produced an ion pair, eV
n = 10**5; # Number of ion pair produced
e = 1.6e-019; # Charge of an electron, C

#Calculations
E_k = E_p*n/10**6; # Kinetic energy of the proton, MeV
A = n*e; # The amount of charge collected on each plate, C

#Results
print "The kinetic energy of the proton = %3.1f MeV \n The amount of charge collected on each plate =  %3.1e C "%(E_k,A)

The kinetic energy of the proton = 3.5 MeV
The amount of charge collected on each plate =  1.6e-14 C


## Example 7.4.1, Page 310¶

In [4]:
#Variable declaration
E_p = 30; # Energy required to produced an ion pair, eV
M = 1000; # Multiplication factor
e = 1.6e-019; # Charge of an electron, C
t = 10**-3; # Time, s
R = 10**5; # Resistance, ohm
E_k = 20*10**6; # Kinetic energy of the proton, eV

#Calculations
n = E_k/E_p; # Number of ion pairs produced
n_a = n*M; # Number of ion-pair after multiplication
Q = n_a*e; # Charge carried by these ion, C
I = Q/t; #  The current through 100-ohm resistance, A
A = I*R; # ,The amplitude of voltage pulse, V

#Results
print "The current through 100-ohm resistance = %6.4e A \n The amplitude of voltage pulse = %6.4e V "%(I, A)

The current through 100-ohm resistance = 1.0667e-07 A
The amplitude of voltage pulse = 1.0667e-02 V


## Example 7.4.2, Page 310¶

In [5]:
import math

#Variable declaration
V = 1500; # Potential difference, V
a = 0.0001; # Radius of the wire, m
b = 0.02; # Radius of the cylinderical tube, m
r = 0.0001; # Distance of electric field from the surface, m

#Calculations
E_r = V/(r*math.log(b/a)); # the electric field at the surface, V/m

#Result
print "The electric field at the surface : %4.2e V/m"%E_r

The electric field at the surface : 2.83e+06 V/m


## Example 7.5.1, Page 311¶

In [6]:
import math

#Variable declaration
V = 2000; # Potential difference, V
a = 0.01; # Radius of the wire, cm
b = 2; # Radius of the cylinderical tube, cm
r = 0.01; # Radius of the wire, m

#Calculations
E_r = V/(r*math.log(b/a)); # the electric field at the surface, V/m

#Result
print "The electric field at the surface : %d V/cm"%E_r

The electric field at the surface : 37747 V/cm


## Example 7.5.2, Page 312¶

In [7]:
#Variable declaration
n_t = 10.0**9; # Total number of counts
n_d = 2000*3*60; # Count recorded per day

#Calculations
n_y = n_d*365; # Counts recorded in 365-days
t = n_t/n_y; # The life of G.M. counter, year

#Result
print "The life of G.M. counter : %4.2f year"%t

The life of G.M. counter : 7.61 year


## Example 7.5.3, Page 312¶

In [8]:
#Variable declaration
E_p = 30; # Energy required for one electron pair, eV
E = 10e+06 ; # Energy lost by alpha particle, eV
n = E/E_p; # Number of ion-pairs produced
M = 5000; # Multiplication factor
C = 50e-012; # Capacitance, F

#Calculations
n_M = n*M; # Number of ion-pairs after multiplication
e = 1.6e-019; # Charge of an electron, C
Q = n_M*e; # Charge present in each ion
A = Q/C; # Amplitude of voltage pulse, V

#Result
print "Amplitude of voltage pulse : %3.1f V"%A

Amplitude of voltage pulse : 5.3 V


## Example 7.5.4, Page 312¶

In [9]:
#Variable declaration
n = 30000; # Count per minute
n_o = n/60; # Observed count rate, count/s
t = 2e-04; # Dead time, s

#Calculations
n_t = round(n_o/(1-n_o*t)); # The true count rate, count/s

#Result
print "The true count rate : %d counts/s"%n_t

The true count rate : 556 counts/s


## Example 7.6.1, Page 313¶

In [10]:
#Variable declaration&Calculations
# For 511 KeV gamma rays (for channel first)
F_W_H_M_1 = 97.; #  Frequency width at half maximum for channel first
P_pos_1 = 1202.; # Peak position for channel first
Res_KeV_1 = F_W_H_M_1/P_pos_1*511; # Resolution in KeV for channel first
# For 1275 KeV gamma rays (for channel second)
F_W_H_M_2 = 82.; # Frequency width at half maximum for channel second
P_pos_2 =  1202.; # Peak position for channel second
Res_KeV_2 = round(F_W_H_M_2/P_pos_2*1275); # Resolution in KeV for channel second

#Results
print "Resolution  for channel first  = %d KeV  \n Resolution  for channel second  = %d KeV "%(Res_KeV_1, Res_KeV_2)

Resolution  for channel first  = 41 KeV
Resolution  for channel second  = 87 KeV


## Example 7.6.2, Page 314¶

In [11]:
#Variable declaration
e = 1.6e-019; # Charge of an electron, C
n = 4.2e+08; # Number of photoelectrons
C = 200e-012; # Capacitance, F

#Calculations
A = n*e/C; # Amplitude of output voltage pulse, V

#Result
print "Amplitude of output voltage pulse : %4.2f V "%A

Amplitude of output voltage pulse : 0.34 V


## Example 7.6.3, Page 315¶

In [12]:
#Variable declaration
F_W_H_M = 0.72; # Full width at half maximum, V
P_p = 6.0; # Peak position, V
E = 662; # Energy of photopeak, KeV

#Calculations
per_resolution = F_W_H_M/P_p*100; # Percentage resolution in percent
Res_KeV = per_resolution/100*E; # Resolution in KeV for Cs-137

#Results
print "The percentage resolution = %d percent \n Resolution in KeV  = %4.1f KeV  "%(per_resolution, Res_KeV)

The percentage resolution = 12 percent
Resolution in KeV  = 79.4 KeV


## Example 7.7.1, Page 316¶

In [13]:
#Variable declaration
E_r = 12; # Relative permittivity
E_o = 8.85e-012; # Permittivity of free space
E = E_r*E_o; # Absolute dielectric constant
C = 100e-012; # Capacitance of the dielectric, F
A = 1.6e-04; # Area of the detector, m^2
e = 1.602e-019; # Charge of an electrin, C
E_p = 3.2; # Energy required to create an ion pair, eV
E_s = 12e+06; # Energy required to stopped ion pair, eV

#Calculations
n = E_s/E_p; # Number of ion-pair produced
Q = n*e; # Charge of these ion pair, C
d = A*E/(C*10**-6); # The thickness of the depletion layer, micron
A = Q/C*1000; # The amplitude of voltage pulse, mV

#Results
print "The thickness of the depletion layer = %d micron \n  The amplitude of voltage pulse: = %6.4f mV  "%(d, A)

The thickness of the depletion layer = 169 micron
The amplitude of voltage pulse: = 6.0075 mV


## Example 7.7.2, Page 316¶

In [14]:
#Variable declaration
E_r = 12; # Relative permittivity
E_o = 8.85e-012; # Permittivity of free space
E = E_r*E_o; # Absolute dielectric constant
A = 2e-04; # Area of the detector, m^2
e = 1.602e-019; # Charge of an electron, C
d = 100e-06; # The thickness of the depletion layer, m
E_p = 3.0; # Energy required to create an ion pair, eV
E_s = 5.48e+06; # Energy required to stopped ion pair, eV

#Calculations
C = E*A/d; # The capacitance of the dielectric, F
n = E_s/E_p; # Number of ion-pair produced
Q = n*e; # Charge of these ion pair, C
A = Q/C*1000; # The amplitude of voltage pulse, mV

#Results
print "The capacitance of dielectric = %5.3e F \n The amplitude of voltage pulse = %5.3f mV"%(C, A)

The capacitance of dielectric = 2.124e-10 F
The amplitude of voltage pulse = 1.378 mV