import math
# Variables
Eg_k = 5.; #kinetic energy of alpha particles(in MeV)
Eg_K = 5.*(10**6)*1.6*(10**-19); #kinetic energy of alpha particles(in J)
mv2 = 2.*Eg_K;
pi = 22./7;
phi = 180.; #firing angle
Z = 29.; #Atomic number
# Calculation
e = 1.6*(10**-19); #electron charge(in C)
Eo = 8.85*10**-12; #permittivity of free space
d = (Z*e**2/(2*pi*Eo*mv2))*(1+1) #;
# Results
print 'distance of the closest approach alpha particles from the copper nucleus(in meter) = %.3e'%d
import math
# Variables
e = 1.6*10**(-19); #electron charge(in C)
m = 9.1*10**(-31); #mass of electron(in Kg)
E_o = 8.854*10**(-12); #permittivity of free space
h = 6.625*10**(-34); #Planck constant
n = 1; #Orbit number
Z = 1; #atomic number
pi = 22./7;
# Calculation and Results
r_1 = (E_o*n**2*h**2)/(pi*m*Z**2*e**2); #first orbit radius of hydrogen atom
print 'first orbit radius of hydrogen atom(in m) = %.4e'%r_1
Freq = m*(Z**2)*(e**4)/(4*(E_o**2)*(n**3)*h**3); #
print 'Orbital frequency of electron(in Hz) = %.4e'%Freq
import math
# Variables
Z_1 = 1; #atomic number for hydrogen
n_1 = 1; #first orbit
r_1 = 0.529; #radius of first orbit of electron for hydrogen
Z_2 = 2; #atomic number for helium
n_2 = 2; #second orbit
# Calculation
k = r_1*Z_1/n_1;
r_2 = k*((n_2)**2)/Z_2; #radius of first orbit of electron for helium
# Results
print 'radius of the second bohr orbit in a math.singly ionized helium atom(in A) = ',r_2
import math
# Variables
n_1 = 1; #first orbit
n_2 = 2; #second orbit
n_3 = 3; #third orbit
# Calculation
#E_1 = -13.6*(Z**2)/(1**2);
#E_2 = -13.6*(Z**2)/(2**2);
#E_3 = -13.6*(Z**2)/(3**2);
#E_3-E_1 = -13.6*(Z**2)*(-8/9);
#E_2-E_1 = -13.6*(Z**2)*(-3/4);
E_1 = -13.6/(1**2); #energy of electron in the first bohr orbit of an atom
E_2 = -13.6/(2**2); #energy of electron in the second bohr orbit of an atom
E_3 = -13.6/(3**2); #energy of electron in the third bohr orbit of an atom
# Results
print 'ratio of energy released = %.4f'%((E_3-E_1)/(E_2-E_1))
import math
# Variables
m = 9.1*10**(-31); #electron mass (in Kg)
Z = 1; #atomic number
e = 1.6*10**(-19); #electron charge(in C)
E_o = 8.25*10**(-12); #permittivity of free space
n = 1; #first bohr orbit
# Calculation
h = 6.63*10**(-34); #planck consmath.tant
R_ps = m*(e**4)/(4*(E_o**2)*(h**3)); #number of revolutions per second
# Results
print 'revolutions per second of an electron in the bohr orbit of hydrogen atom = %.3e'%R_ps
# rounding off error
import math
# Variables
n = 1.; #first bohr orbit
Z = 1.; #atomic number
# Calculation
m = 9.1*10**(-31); #electron mass in Kg.
e = 1.6*10**(-19); #electron charge(in C)
E_o = 8.85*10**(-12); #permittivity of free space
h = 6.63*10**(-34); #planck constant
v_n = m*(Z**2)*(e**4)/(4*(E_o**2)*(h**3)*(n**3)); #orbital frequency of an electron in the first bohr orbit in a hydrogen atom
# Results
print 'orbital frequency of an electron in the first bohr orbit in a hydrogen atom(in Hz) = %.3e'%v_n
# rounding off error
import math
# Variables
m = 9.11*10**-31; #mass of electron(in Kg)
Z = 1; #atomic number
n = 1; #first bohr orbit
# Calculation
E_o = 8.854*10**-12; #permittivity of free space
h = 6.625*10**-34; #planck consmath.tant
e = 1.6*10**-19; #electron charge(in C)
E_k = (m*(Z**2)*(e**4))/(8*(E_o**2)*(n**2)*(h**2)); #Kinetic energy(in joule)
E = E_k/e; #Kinetic energy(in eV)
E_t = -13.6*(Z**2/n**2); #Total Energy(in eV)
E_p = E_t-E; #Potential energy(in eV)
# Results
print 'Total energy in = %.1f eV'%E_t
print 'kinetic energy in = %.1f eV'%E
print 'potential energy in = %.1f eV'%E_p
import math
# Variables
h = 6.626*10**-34; #planck consmath.tant
E_o = 8.825*10**-12; #permittivity of free space
e = 1.6*10**-19; #electron charge(in C)
n = 1; #first bohr orbit
Z = 1; #atomic number
# Calculation
v = Z*(e**2)/(2*E_o*n*h); #velocity of electron in hydrogen atom in bohr first orbit
# Results
print 'velocity of electron in hydrogen atom in bohr first orbit(in meter/sec) = %.3e'%v
import math
# Variables
n_1 = 1.; #electron excited from ground state
h = 6.62*10**-34; #Planck consmath.tant
c = 3.*10**8; #speed of light
E_o = 8.825*10**-12; #permittivity of free space
e = 1.6*10**-19; #electron charge(in C)
m = 9.11*10**-31; #mass of electron(in Kg)
E_1 = 10.2; #energy excites the hydrogen from ground level(in eV)
# Calculation and Results
K = m*e**4/(8*(E_o**2)*(h**2)) #in joule
K_e = K/e; #in eV
#E_1 = K_e*((1/n_1**2)-(1/n**2))
#1/(n**2) = 1/(n_1**2)-E_1/K_e
#n**2 = 1/(1/(n_1**2)-E_1/K_e)
n = (1/(1/(n_1**2)-E_1/K_e))**(1./2); #principal quntum number when 10.2 eV energy excites electron
print 'principal quntum number when 10.2 eV energy excites electron = %.f'%(n)
W_1 = h*c/(E_1*e)*10**10; #wavelength of radiation when 10.2 eV energy excites electron
print 'wavelength of radiation when 10.2 eV energy excites electron(in A) = %d'%W_1
E_2 = 12.09; #energy excites the hydrogen from ground level(in eV)
n_2 = (1./(1./(n_1**2)-E_2/K_e))**(1./2); #principal quntum number when 12.09 eV energy excites electron
W_2 = h*c/(E_2*e)*10**10; #wavelength of radiation when 12.09 eV energy excites electron
print 'principal quntum number when 12.09 eV energy excites electron = %.f'%(n_2)
print 'wavelength of radiation when 12.09 eV energy excites electron in = %d A'%W_2
import math
# Variables
At_w = 63.54; #atomic weight of copper
N = 6.023*10**23; #avogadro's number
# Calculation
W_a = At_w/N; #weight of one atom(in gm)
W_p = W_a/63; #weight of one proton(in gm)
# Results
print 'weight of one atom in %.3e gm'%W_a
print 'weight of one proton in %.3e gm'%W_p
import math
# Variables
Atw_Cu = 63.54; #atomic weight of copper
Atw_Si = 28.09; #atomic weight of silicon
# Calculation
# 5 atoms of copper working in Cu_5_Si
Tw_Cu = 5*Atw_Cu; #total weight of copper used in copper silicide
Tw_Si = Atw_Si; #total weight of silicon used in copper silicide
Percentage = (Tw_Si/(Tw_Cu+Tw_Si))*100; #percentage of Si in Copper silicide
# Results
print 'percentage of Si in Copper silicide Cu_5_Si is = %.2f %%'%Percentage