#initiation of variable
from math import sqrt, pi
R=0.1;Z=79.0; x=1.44; #x=e^2/4*pi*epsi0
zkR2=2*Z*x/R # from zkR2= (2*Z*e^2)*R^2/(4*pi*epsi0)*R^3
mv2=10.0*10**6; #MeV=>eV
#calculation
theta=sqrt(3.0/4)*zkR2/mv2; #deflection angle
theta=theta*(180/pi); #converting to degrees
#result
print"Hence the average deflection angle per collision in degrees is",round(theta,3 );
#initiation of variable
from math import sin, cos, tan, sqrt, pi
Na=6.023*10**23;p=19.3;M=197.0;
n=Na*p/M; #The number of nuclei per atom
t=2*10**-6;Z=79;K=8*10**6;x=1.44; theta=90.0*pi/180; #x=e^2/4*pi*epsi0
b1=t*Z*x/tan(theta/2)/(2*K) #impact parameter b
f1=n*pi*b1**2*t #scattering angle greater than 90
#result
print"The fraction of alpha particles scattered at angles greater than 90 degrees is %.1e" %f1;
#part b
theta=45.0*pi/180;
b2=t*Z*x/tan(theta/2)/(2*K);
f2=n*pi*b2**2*t; #scattering angle greater than 45
fb=f2-f1 #scattering angle between 45 to 90
#result
print"The fraction of particles with scattering angle from 45 to 90 is %.1e" %fb;
#initiation of variable
from math import sin, cos, tan, sqrt, pi
Z=79.0;x=1.44;K=8.0*10**6;z=2; #where x=e^2/4*pi*epsi0;z=2 for alpha particles
#calculation
d=z*x*Z/K; #distance
#result
print "The distance of closest approach in nm. is",d*10**-9
#initiation of variable
sl=820.1;n0=3.0; #given values
n=4;w=sl*(n**2/(n**2-n0**2));
#result
print "The 3 longest possible wavelengths in nm respectively are a.",round(w,3),;
#partb
n=5.0;w=sl*(n**2/(n**2-n0**2));
#result
print "b. (in nm)",round(w,3),;
#partc
n=6.0;w=sl*(n**2/(n**2-n0**2));
#result
print "c. (in nm )",round(w,3);
#initiation of variable
sl=364.5;n=3.0; #given variables and various constants are declared in the subsequent steps wherever necessary
w1=sl*(n**2/(n**2-4)); #longest wavelength of balmer
c=3.0*10**8;
f1=c/(w1*10**-9); #corresponding freq.
n0=1.0;n=2.0;
#calculation
w2=91.13*(n**2/(n**2-n0**2)); #first longest of lymann
f2=c/(w2*10**-9); #correspoding freq
n0=1.0;n=3.0
w3=91.13*(n**2/(n**2-n0**2)); #second longest of lymann
f3=3.0*10**8/(w3*10**-9) #corresponding freq.
#result
print "The freq. corresponding to the longest wavelength of balmer is %.1e" %f1," & First longest wavelength of Lymann is %.1e" %f2;
print"The sum of which s equal to %.1e" %(f1+f2);
print"The freq. corresponding to 2nd longest wavelength was found out to be %.1e" %f3,"Hence Ritz combination principle is satisfied.";
#initiation of variable
Rinfi=1.097*10**7; #known value
n1=3.0;n2=2.0; #first 2 given states
#calculation
w=(n1**2*n2**2)/((n1**2-n2**2)*Rinfi);
#result
print"Wavelength of transition from n1=3 to n2=2 in nm is",round(w*10**9,3);
#partb
n1=4.0;n2=2.0; #second 2 given states
w=(n1**2*n2**2)/((n1**2-n2**2)*Rinfi);
#result
print"Wavelength of transition from n1=3 to n2=2 in nm is",round(w*10**9,3);
#initiation of variable
n1=3.0;n2=2.0;Z=4.0;hc=1240.0;
delE=(-13.6)*(Z**2)*((1/(n1**2))-((1/n2**2)));
#calculation
w=(hc)/delE; #for transition 1
#result
print "The wavelngth of radiation for transition(2->3) in nm is", round(w,3);
#for transition 2
n1=4.0;n2=2.0; # n values for transition 2
delE=(-13.6)*(Z**2)*((1/n1**2)-(1/n2**2));
w=(hc)/delE;
#result
print "The wavelngth of radiation emitted for transition(2->4) in nm is", round(w,3);