# Two approximations to Planck's Law are useful in the extreme low and high limits of (lambda T).

## Question:

Two approximations to Planck's Law are useful in the extreme low and high limits of \(\lambda T\).

**a.** Show that in the limit where \(\left(C_{1} / \lambda T\right) \gg 1\) that Planck's spectral distribution reduces to the following form:

\[E_{b \lambda}(\lambda, T) \approx \frac{C_{o}}{\lambda^{5}} \exp \left(-\frac{C_{1}}{\lambda T}\right) \quad \text { Wien's Law }\]

Compare this result to Planck's distribution and determine when the error between the two is less than \(1 \%\).

**b.** Show that in the limit \(\left(C_{1} / \lambda T\right) \ll 1\) Planck's distribution law reduces to:

\[E_{b \lambda}(\lambda, T) \approx C_{2} \frac{T}{\lambda^{4}} \quad \text { Rayleigh-Jeans Law }\]

Compare with Planck's distribution and determine when the two are in error by less than \(1 \%\).

## Step by Step Answer:

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