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## Homework Statement

The power delivered in narrow spectrum range near 10 µm from black body source with temperature 1000 K is 10 µW.

**Not Solved**a) What power would be delivered in narrow spectrum range near 1 µm?

__Solved__b) At what wavelength the power delivered takes its maximum?

c) Find this maximum value.

## Homework Equations

For b and c, you are using:

λ

_{peak}= 2.898 x 10

^{-3}/T

That aspect of this problem is easy and was solvable.

For a, I would assume that one would use:

P = σAT

^{4}

Problem is that the question doesn't give surface area at all, only λ. Plugging what was given doesn't produce the relationship at all (even squaring the given λ = 10 µm only produces 5.6 µW). I don't know if it is a bad question or missing something obvious.

I also tried E = σT

^{4}and got 5.7 W/cm

^{2}. I would assume that I would have to calculate per 1 µm?

The other alternative solution I tried was using Radiant flux density (Planck’s law):

W = 2hc

^{2}/λ

^{5}x 1/(e

^{(hc/λkT)}-1) and the numbers still seem off.

## The Attempt at a Solution

From above.

Also, based on the information above and solving part b and c that moving closer to the black body (2.898 µm) will produce the highest power and would dip off after as we approach 1 µm, but it feels like there is something missing in part a.

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