Plot Plank’s law for black body radiation and compare it with Raleigh- jeans law at high temperature and low temperature

AIM:- Plot Plank’s law for black body radiation and compare it with Raleigh- jeans law at high temperature and low temperature .

THEORY :-

1.Plank’s radiation law :- Wien displacement law and Rayleigh jeans formula could not explain the entire shape of the cures giving the energy distribution in black body radiation . To explain the entire shape, plank in the beginning imagined that a black radiation chamber is filled up not only with radiation but also with the molecules of a perfect gas . Planck gave anew revolutionary idea which laid the foundation of the modern quantum theory.  udr = 8𝜋h𝑐 ∗ 𝑑𝑟𝑟5 exp ( h𝑐 ) − 1 𝑟𝑘𝑡   2. Rayleigh jeans law:- The deduction of Rayleigh law for the distribution of energy in the normal spectrum has been done by assuming of that the energy is equally dividedamong all the possible motes of vibration.udr = 8𝜋𝑟𝑘𝑡 𝑑𝑟 4

Algorithm :- 

1. Start the Sci lab software and write the all given input values of constant h, k, c, etc.

2. Gives the different values of temp. in Kelvin .
3. Using the linspace command for define the range .
4. Using the for loop for discrete the no. of particle.
5. Give the for loop for temperature.
6. Write the equation of plank ,Rayleigh and Wien’s law.
7. Using the subplot command and plot the graph of plank , Rayleigh And comparing between the plank and Rayleigh law.
   
8. And finally comparing between the plank ,Rayleigh and weins law.
9. Using the legend command for comment on graph and using xgrid command .

Programe:-

clc
clf
h=6.626e-34 //planks constant k=1.38e-23 //boltzmann constant c=3e8 //speed of light t=[1000,1200,1400] //temp (KELVIN) n=1400
r=linspace(0.1e-6,15e-6,n) r0=linspace(5e-6,15e-6,n) for i=1:n
for j=1:3 u(j,i)=(8*%pi*h*c)/((r(i))^5*(exp(h*c/(r(i)k*t(j)))-1)) m(j,i)=(8%pi*k*t(j))/(r0(i))^4 v(j,i)=(8*%pi*h*c)/((r(i))^5*(exp(h*c/(r(i)*k*t(j)))))
end
end
subplot(2,2,1)
plot(r,u(1,:),'r')
plot(r,u(2,:),'g')
plot(r,u(3,:),'b') xlabel("Wavelength--->","fontsize",3) ylabel("Energy--->","fontsize",3) title("Planks law","fontsize",3) legend("T1=1000","T2=1200","T3=1400") xgrid
subplot(2,2,2)
plot(r0,m(1,:),'r')
plot(r0,m(2,:),'g')
plot(r0,m(3,:),'b') xlabel("Wavelength--->","fontsize",3) ylabel("Energy--->","fontsize",3) title("Rayleigh law","fontsize",3) legend("T1=1000","T2=1200","T3=1400") xgrid
subplot(2,2,3) plot(r,u(3,:),'b') plot(r0,m(3,:),'g')
                      
xlabel("Wavelength--->","fontsize",3)
ylabel("Energy --->","fontsize",3)
title("Compare b/w Planks and Rayleigh law","fontsize",3) legend("(PLANKS)","(RAYLEIGH)") xstring(1.2e-05,500,"T=1200 K")
xgrid
subplot(2,2,4)
plot(r,u(3,:),'r')
plot(r0,m(3,:),'g')
plot(r,v(3,:),'b--')
xlabel("Wavelength --->","fontsize",3)
ylabel("Energy --->","fontsize",3)
title("Compare b/w Planks,Rayleigh law and Weins law ","fontsize",3) legend("Planks=r","Rayleugh jeans=g","Weins=b") xstring(1.2e-05,450,"T=1200 K")
xgrid

Results:-

1. Rayleigh jeans used classical physics to explain black body Spectrum .This law hold good at higher wavelength but is in complete disagreement with experimental data, for shorter wavelength .This is failure is k/a UV catastrophe because energy density tends to infinity after visible region or in UV region.
2. The plank’s law fully explain the black body Spectrum, be used the Concept of quantum mechanics. That the energy exchanged b/w the radiation and matter is not continuous indeed it is discrete.
3. Wien’s law is in good agreement with the experimental result for shorter wavelength but it deviates for longer wavelength.