# Chapter 3:Atomic Spectra-III¶

## Example no:4,Page no:485¶

In [15]:
#Variable declaration
R=109729.0                                                                        #(cm-1)
T1=43487.0                                                                        #(cm-1)
T2=28583.0                                                                        #(cm-1)
n=2.0

#calculation
import math
delta=n-math.sqrt(R/T2)                                                              #quantum defect

#Result
print"\nquantum defect =",round(delta,4)

quantum defect = 0.0407


## Example no:5,Page no:485¶

In [43]:
#Variable declaration
R=109737                                                                        #(cm-1)
n=1.805                                                                         #effective quantum number for the ground state of rubidium

#calculation
T=R/(8065*n**2)                                                                  #ionization potential of rubidium (eV)

#Result
print"The ionization potential of rubidium =",round(T,3),"eV"

The ionization potential of rubidium = 4.176 eV


## Example no:6,Page no:485¶

In [44]:
#Variable declaration
ratio=2.5                                                                       #ratio of ionization potential of hydrogen and sodium
n=3.0

#calculation
import math
z=math.sqrt(n**2/ratio)                                                               #effective atomic number of sodium

#Result
print"\nEffective atomic number of sodium =",round(z,2)

Effective atomic number of sodium = 1.9


## Example no:7,Page no:485¶

In [45]:
#Variable declaration
hc=12400.0                                                                        #value of product of plank's constant and speed of light (eV Å)
E1=3.18                                                                         #separation of 4s and 3s level (eV)
lembda=5890.0                                                                     #wavelength of the first member of principal series of sodium (Å)

#calculation
E2=round(hc/lembda,1)                                                                    #separation of 3s and 3p levels (eV)
deltaE=E1-E2                                                                    #separation of 4s and 3p level (eV)
lembda1=hc/deltaE                                                               #wavelength of the first member of sharp series (Å)

#Result
print"λ =%d"%lembda1,"Å"

λ =11481 Å


## Example no:8,Page no:486¶

In [46]:
#Variable declaration
lembda1=5890*10**-10                                                             #wavelength of doublet (Å)
lembda2=5896*10**-10                                                             #wavelength of doublet (Å)
h=6.63*10**-34                                                                   #Plank's constant (Js)
c=3*10**8                                                                        #speed of light (m/s)
e=1.6*10**-19                                                                    #Charge of electron (coulombs)

#calculation
deltaV=(lembda2-lembda1)/(lembda1*lembda2)                                      #wave no. (m-1)
deltaE=(h*c*deltaV)/e                                                           #separation of energy levels (eV)

#Result
print"ΔE =%.2e"%deltaE,"eV"

ΔE =2.15e-03 eV


## Example no:9,Page no:486¶

In [47]:
#Variable declaration
deltaT=2.1*10**-3                                                                #(eV)
lembda=5893*10**-8                                                               #(Å)

#calculation
deltaV=deltaT*8065                                                              #(cm-1)
deltalembda=deltaV*lembda**2                                                     #(cm)

#Result
print"Δλ =%.2e"%deltalembda,"cm"

Δλ =5.88e-08 cm


## Example no:10,Page no:486¶

In [48]:
#Variable declaration
E1=16960.0                                                                        #mean position of the level (cm-1)
E2=24490                                                                        #convergence limit of sharp series (cm-1)

#calculation
I=(E1+E2)/8065.0                                                                  #ionization energy of sodium atom (eV)

#Result
print"I =",round(I,4),"eV"

I = 5.1395 eV


## Example no:11,Page no:486¶

In [49]:
#Variable declaration
E1=41450.0                                                                        #principal series for sodium atom (cm-1)
E2=24477.0                                                                        #sharp series for sodium atom (cm-1)

#calculation
I=(E1)/8065.0                                                                  #ionization energy of sodium atom (eV)

print"\nI =",round(I,3),"eV"

I = 5.139 eV


## Example no:12,Page no:487¶

In [50]:
#Variable declaration
E1=14904                                                                        #mean position of the level (cm-1)
E2=28583                                                                        #convergence limit of sharp series (cm-1)

#calculation
I=(E1+E2)/8065.0                                                                  #ionization energy of Li atom (eV)

#Result
print"I =",round(I,2),"eV"

I = 5.39 eV


## Example no:13,Page no:487¶

In [51]:
#Variable declaration
R=109734                                                                        #(cm-1)
T=24477.0                                                                         #(cm-1)
Zeff=1
n=3

#calculation
import math
delta=n-(Zeff*math.sqrt(R/T))                                                        #quantum defect for 3p configuration of sodium

#Result
print"\nΔ =",round(delta ,3)

Δ = 0.883


## Example no:14,Page no:487¶

In [42]:
#Variable declaration
z1=1.0                                                                            #atomic no.
z2=2.0                                                                            #atomic no.
deltaT2=5.84                                                                    #doublet splitting of the first excited state for z=2 (cm-1)

#calculation
deltaT1=deltaT2*(z1/z2)**4                                                       #separation in hydrogen atom (cm-1)

#Result
print"Separation in hydrogen atom =",deltaT1,"cm**-1"

Separation in hydrogen atom = 0.365 cm**-1