#Variable declaration
z=2 #atomic no. of He
a0=0.529 #radius of first Bohr orbit of H atom (Å)
n=1 #no. of Bohr orbit
A=2.19*10**6 #velocity of e in first Bohr orbit of H atom (m/s)
B=4.14*10**15 #orbital frequency in the first Bohr orbit of H atom (rad/s)
E0=13.6 #energy of electron in ground state of H atom (eV)
n1=1
n2=2
R=1.097*10**7 #Rydberg constant (m-1)
#Calculation
#(i) radius of first Bohr orbit
r=a0/2.0 #radius of first Bohr orbit (Å)
#(ii) velocity of electron in the first orbit
v=A*(z/n) #velocity of electron in the first orbit (m/s)
#(iii) orbital frequency in the first orbit
omega=B*(z**2/n**3) #orbital frequency in the first orbit (rad/s)
#(iv) kinetic and binding energy
KE=E0*(z**2/n**2) #kinetic energy of electron in the ground state (eV)
BE=KE #binding energy of electron in the ground state (eV)
#(v) ionization potential and first excitation potential
IP=KE #ionization potential (eV)
EE=E0*z**2*((1.0/n1**2)-(1.0/n2**2)) #first excitation potential (eV)
#(vi) wavelength of the resonance line emitted in the transition n=2 to n=1
lembda=(1.0/(R*z**2*((1.0/n1**2)-(1.0/n2**2))))*10**10 #wavelength of the resonance line emitted in the transition n=2 to n=1 (Å)
#Result
print"\n(i) radius =",round(r,3),"Å"
print"(ii) velocity =%.2e"%v,"m/s"
print"(iii) orbital frequency =",omega,"rad/s"
print"(iv) Kinetic energy =",KE,"eV Binding energy =",BE,"eV"
print"(v) Ionization potential =",IP,"eV EE =",EE,"eV"
print"(vi) wavelength =",lembda,"Å"
#Variable declaration
z=1 #atomic no. of H atom
m=1.68*10**-27 #mass of H atom (kg)
h=1.054*10**-34 #Planck's constant (joule second)
R=10967800 #Rydberg constant (m-1)
e=1.6*10**-19 #Charge of electron (coulombs)
c=3*10**8 #speed of light (m/s)
#Calculation
import math
#(i) recoil velocity
v=(3*math.pi*h*R*z**2)/(2*m) #recoil velocity of H atom (m/s)
#(ii) recoil kinetic energy
Er=(9/8.0)*((math.pi*h*R*z**2)**2/(m*e)) #recoil kinetic energy of H atom (eV)
#(iii) energy of emitted photon
E=(1.5*math.pi*h*c*R*z**2)/e #energy of emitted photon (eV)
#Result
print"(i) recoil velocity =",round(v,2),"m/s"
print"(ii) recoil kinetic energy =%.1e"%Er,"eV"
print"(iii) energy of emitted photon =",round(E,2),"eV"
#Variable declaration
z=2 #atomic no. of He atom
h=1.054*10**-34 #Planck's constant (joule second)
R=10967800 #Rydberg constant (m-1)
e=1.6*10**-19 #Charge of electron (coulombs)
c=3*10**8 #speed of light (m/s)
#calculation
E=1.5*math.pi*h*c*R*z**2 #The energy of the emitted photon (J)
IE=2*math.pi*h*c*R #Ionization energy of H atom (J)
KE=(E-IE)/e #Kinetic energy of the photoelectron (eV)
#Result
print"\nKinetic energy of photoelectron =",round(KE,1),"eV"
#Variable declaration
ratio=4 #ratio of wavelengths
z1=1 #atomic no. of hydrogen atom
#calculation
z2=math.sqrt(ratio*z1**2) #atomic no. of unknown element
#Result
print"Atomic no. =",z2,"(helium)"
#Variable declaration
lembda1=108.5*10**-9 #wavelength (m)
lembda2=30.4*10**-9 #wavelength (m)
R=1.097*10**7 #Rydberg constant (m-1)
z=2 #atomic no. of He
n0=1 #ground state
#calculation
import math
n=math.sqrt(1.0/((1.0/n0**2)-(((1.0/lembda1)+(1.0/lembda2))/(R*z**2)))) #quantum no. corresponding to the excited state of He+
#Result
print"n =",round(n )
#Variable declaration
z=2 #atomic no. of He+ ion
lembda=133.7*10**-9 #difference b/w the first lines of the Balmer and Lyman series (m)
n1=1
n2=2
n3=3
#calculation
R=(1.0/(lembda*z**2))*((1.0/((1.0/n2**2)-(1.0/n3**2)))-(1.0/((1.0/n1**2)-(1.0/n2**2)))) #Rudberg constant (m-1)
#Result
print"R =%.3e"%R,"m**-1"
#Variable declaration
R=1.097*10**7 #Rydberg constant (m-1)
lembda=59.3*10**-9 #wavelength difference b/w first lines of Balmer and Lyman series (m)
#calculation
import math
z=math.sqrt(88.0/(15.0*R*lembda)) #atomic no.
#Result
print"Z =",round(z)
#Variable declaration
R=1.097*10**7 #Rydberg constant (m-1)
ratio=1836 #ratio of maas of tritium and hydrogen
#calculation
lembda=(36*2*10**10)/(5*R*3*ratio) #separation of the first line of the Balmer series (Å)
#Result
print"Δλ =",round(lembda,1),"Å"