(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The dependence on wavelength [tex] \lambda [/tex] of the intensity [tex]I(\lambda)d\lambda[/tex] of the radiation emitted by a body which is in thermal equilibrium with its surroundings at temeratureTis given by:

[tex]I(\lambda)d\lambda = \frac{2 \pi h c^{2}/\lambda^5}{e^{hc/kT\lambda}-1}d\lambda[/tex]

in the interval of wavelength between [tex] \lambda [/tex] and [tex] \lambda+d\lambda [/tex]. In this expression,his Planck's constant,kis Boltzmann's constant, andcis the velocity of light.

Sketch and clearly label on one figure the dependences of [tex]I(\lambda)d\lambda[/tex] on [tex] \lambda [/tex] for three different temperatures [tex] T_{1} < T_{2} < T_{3} [/tex].

Simplify the above expression in the limit of (i) short wavelength ([tex]\lambda\rightarrow0[/tex]) and (ii) long wavelength ([tex]\lambda\rightarrow\infty[/tex]).

(The binomial expansion [tex]e^{x} = 1+x+x^{2}/2+...[/tex] may be useful.)

2. Relevant equations

All given in the problem i think.

3. The attempt at a solution

I found Planck's Radiation Law was almost exactly the same as this i searched for it on wikipedia for more information:

http://en.wikipedia.org/wiki/Planck's_law

On that page is a graph which i thought was showing what the first part of the question is asking but i don't understand what the question means when it says "clearly label on one figure the dependences of [tex]I(\lambda)d\lambda[/tex] on [tex] \lambda [/tex]"?

For the second part i tried to make the formula look simpler first:

[tex]\frac{A}{\lambda^{5}(e^{B/\lambda} - 1)}[/tex]

I think as [tex]\lambda\rightarrow0[/tex], [tex]e^{B/\lambda} - 1[/tex] can be simplified to [tex]e^{B/\lambda}[/tex] because the latter expression will be very large giving:

[tex]\frac{A}{\lambda^{5}e^{B/\lambda}}[/tex]

I'm having some trouble posting the rest of my thread but i thought for the last part as lambda goes to infinity the expression would simplify to A/lambda^5 but i'm not sure how to work these out for definite i think this is probably wrong.

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# Homework Help: Planck's Radiation Law?

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