# Chapter 20: X-Ray¶

## Example 20.1, Page 20.7¶

In [2]:
from math import *

# Given
V1 = 40e3 # voltage in first case in V
V2 = 20e3 # voltage in second case in V
V3 = 100e3 # voltage in second in V

#Calculations
v1 = 0.593e6 * sqrt(V1)
lambda1 = 12400 / V1
v2 = 0.593e6 * sqrt(V2)
lambda2 = 12400 / V2
v3 = 0.593e6 * sqrt(V3)
lambda3 = 12400 / V3

#Results
print "Max. speed of electrons at %d Volts is %.3e m/sec\nMax. speed of electrons at %d Volts is %.2e m/sec/sec\nMax. speed of electrons at %d Volts is %.3e m/sec\nShortest wavelength of x-ray = %.2f A\nShortest wavelength of x-ray = %.2f A\nShortest wavelength of x-ray = %.3f A"%(V1,v1,V2,v2,V3,v3,lambda1,lambda2,lambda3)

Max. speed of electrons at 40000 Volts is 1.186e+08 m/sec
Max. speed of electrons at 20000 Volts is 8.39e+07 m/sec/sec
Max. speed of electrons at 100000 Volts is 1.875e+08 m/sec
Shortest wavelength of x-ray = 0.31 A
Shortest wavelength of x-ray = 0.62 A
Shortest wavelength of x-ray = 0.124 A


## Example 20.2, Page 20.7¶

In [3]:

# Given
V = 30e3 # voltage in V
lambda_min = 0.414e-10 # shortest wavelength in m
e = 1.6e-19 # charge on an electron in C
c = 3e8 # speed of light in m/sec

#Calculations
h = (e * V * lambda_min) / c

#Result
print "Planck constant is %.3e J sec"%h

Planck constant is 6.624e-34 J sec


## Example 20.3, Page 20.8¶

In [4]:

# Given
V = 25e3 # voltage in V

#Calculations
lambda_min = 12400 / V

#Result
print "Minimum wavelength of x-ray is %.3f A"%lambda_min

Minimum wavelength of x-ray is 0.496 A


## Example 20.4, Page 20.8¶

In [5]:
from math import *

# Given
V = 13.6e3 # voltage in V

#Calculations
v = 0.593e6*sqrt(V)

#Result
print "Maximum speed of electron is %.2e m/sec"%v

Maximum speed of electron is 6.92e+07 m/sec


## Example 20.5, Page 20.8¶

In [6]:
from math import *

# Given
V = 10e3 # voltage in V
i = 2e-3 # current in amp

#Calculations
v = 0.593e6*sqrt(V)

#Result
print "Velocity of electron is %.2e m/sec"%v

Velocity of electron is 5.93e+07 m/sec


## Example 20.6, Page 20.8¶

In [9]:

# Given
V = 9.8e3 # voltage in V
i = 2e-3 # current in amp
c = 3e8 # speed of light in m/sec

#Calculations
lamda = 12400 / V
f = c / (lamda*10**-10)

#Results
print "Highest frequency is %.2e Hz\nMinimum wavelength is %.2f A"%(f,lamda)

Highest frequency is 2.37e+18 Hz
Minimum wavelength is 1.27 A


## Example 20.7, Page 20.9¶

In [10]:
from math import *

# Given
V = 12.4e3 # voltage in V
i = 2e-3 # current in amp
e = 1.6e-19 # charge on an electron in C

#Calculations
n = i / e
v = 0.593e6*sqrt(V)

#Result
print "Number of electrons striking the target per sec is %.2e\nSpeed of electrons is %.1e m/sec"%(n,v)

Number of electrons striking the target per sec is 1.25e+16
Speed of electrons is 6.6e+07 m/sec


## Example 20.8, Page 20.9¶

In [11]:

# Given
V = 10e3 # voltage in V
i = 15e-3 # current in amp
e = 1.6e-19 # charge on an electron in C

#Calculations
n = i / e
lamda = 12400 / V

#Results
print "Number of electrons striking the anode per sec is %.2e\nMinimum wavelength produced  is %.2f A"%(n,lamda)

Number of electrons striking the anode per sec is 9.38e+16
Minimum wavelength produced  is 1.24 A


## Example 20.9, Page 20.9¶

In [13]:

# Given
V = 50e3 # voltage in V
i = 1e-3 # current in amp
e = 1.6e-19 # charge on an electron in C

#Calculations
n = i / e

#Result
print "Number of electrons striking the anode per sec is %.2e"%n

Number of electrons striking the anode per sec is 6.25e+15


## Example 20.10, Page 20.10¶

In [15]:

# Given
lambda1 = 40e-12 # minimum wavelength in first case in m
lambda2 = 1e-10 # minimum wavelength in second case in m

#Calculations
V1 = 12400e-10 / lambda1
V2 = 12400e-10 / lambda2

#Results
print "Applied voltage to get wavelength of %.e meter is %.f KV\nApplied voltage to get wavelength of %.e meter is %.1f KV"%(lambda1,V1/10**3,lambda2,V2/10**3)

Applied voltage to get wavelength of 4e-11 meter is 31 KV
Applied voltage to get wavelength of 1e-10 meter is 12.4 KV


## Example 20.11, Page 20.10¶

In [16]:

# Given
V1 = 44e3 # voltage in first case in V
V2 = 50e3 # voltage in second case in V
lambda1 = 0.284e-10 # shortest wavelength in first case in m
lambda2 = 0.248e-10 # shortest wavelength in second case in m
e = 1.6e-19 # charge on an electron in C
c = 3e8 # speed of light in m/sec

#Calculations
h1 = e * V1 * lambda1 / c
h2 = e * V2 * lambda2 / c

#Results
print "Planck constant is %.2e J sec if shortest wavelength is %.3e m \nPlanck constant is %.3e Jsec if shortest wavelength is %.3e m "%(h1,lambda1,h2,lambda2)

Planck constant is 6.66e-34 J sec if shortest wavelength is 2.840e-11 m
Planck constant is 6.613e-34 Jsec if shortest wavelength is 2.480e-11 m


## Example 20.12, Page 20.10¶

In [14]:

# Given
lamda = 1e-11 # K-absorption limit for uranium in m

#Calculations
V = 12400e-10 / lamda

#Result
print "Excitation potential is %d kV"%(V/10**3)

Excitation potential is 124 kV


## Example 20.13, Page 20.11¶

In [17]:

# Given
lamda = 1.4e-11 # K-absorption edge for lead in m
V = 88.6e3 # minimum voltage required for producing k-lines in V
c = 3e8 # speed of light in m/sec

#Calculations
r = V * lamda / c

#Result
print "The value of the ratio of h/e = %.3e Jsec/C"%r

The value of the ratio of h/e = 4.135e-15 Jsec/C


## Example 20.14, Page 20.11¶

In [18]:

# Given
Z = 92 # atomic no. of atom
Rh = 1.1e5 # Rydberg constant in cm^-1
c = 3e8 # speed of light in m/sec

#Calculations
lamda = 1 / (Rh *(Z-1)**2 * (1 - (1 / 2**2)))

#Result
print "Wavelength of K line = %.2f A"%(lamda*1e8)

Wavelength of K line = 0.11 A


## Example 20.15, Page 20.11¶

In [19]:

# Given
Z = 42 # atomic no. of Mo
lamda = 0.71e-10 # wavelength in m
Z_ = 29 # atomic no. of Cu

#Calculations
lambda_ = (Z-1)**2 * lamda / (Z_-1)**2

#Result
print "Wavelength of the corresponding radiation of Cu is %.2f A"%(lambda_*1e10)

Wavelength of the corresponding radiation of Cu is 1.52 A


## Example 20.16, Page 20.12¶

In [20]:

# Given
Z = 79 # atomic no. of element
b = 1 # a constant
a = 2.468e15 # a constant in per sec
c = 3e8 # speed of light in m/sec

#Calculations
f = a * (Z - b)**2
lamda = c / f

#Result
print "Wavelength of x-ray is %.4f A"%(lamda*1e10)

Wavelength of x-ray is 0.1998 A


## Example 20.17, Page 20.12¶

In [22]:

# Given
Z = 29 # atomic no. of Cu
R = 1.097e7 # Rydberg constant in m^-1
c = 3e8 # speed of light in m/sec
h = 6.62e-34 # Planck constant in J sec

#Calculations
f = 3./4 * (R * c) * (Z-1)**2
E = h * f / 1.6e-16
E_L = 0.931 # let E_L = 0.931 KeV
E_ = E + E_L

#Result
print "Ionization potential of K-shell electron of Cu is %.3f keV"%E_

Ionization potential of K-shell electron of Cu is 8.938 keV


## Example 20.18, Page 20.13¶

In [23]:

# Given
Z = 79 # atomic no. of anticathode
R = 1.097e7 # Rydberg constant in m^-1
c = 3e8 # speed of light in m/sec

#Calculations
f = 3./4 * (R * c) * (Z-1)**2

#Result
print "Frequency of k line is %.3e Hz"%f

Frequency of k line is 1.502e+19 Hz


## Example 20.19, Page 20.13¶

In [24]:

# Given
Z = 27 # atomic no. of Co
R = 1.097e7 # Rydberg constant in m^-1
c = 3e8 # speed of light in m/sec
h = 6.62e-34 # Planck constant in J sec

#Calculations
f = 3./4 * (R * c) * (Z-1)**2
E = h * f
lamda = c / f

#Results
print "Energy is %.2f keV\nWavelength of x-ray is %.2f A"%(E / 1.6e-16,lamda*1e10)

Energy is 6.90 keV
Wavelength of x-ray is 1.80 A