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## Homework Statement

The first unmanned probe will reach the stellar system of the Alfa Centauri (estimated radius 5x10

^{4}

km) in year 2145. The probe will enter stationary orbit of radius R 300 x10

^{6}km around the

star. In order to power itself the probe will convert the radiative energy received by its 10m

^{2}

antenna. It is estimated that when oriented at a right angle with respect to the incoming radiation,

the antenna will collect 30000W of total radiative power. From given information one may infer

that the λmax wavelength for which the Alfa Centauri emits the most energy, is:

a) 253nm

b) 105nm

c) 332nm

d) 78nm

e) information provided is insufficient to solve this problem

## Homework Equations

E=hf

v=fλ

## The Attempt at a Solution

I thought to approach this problem by first finding the amount of energy (in joules, rather than watts) that the antenna would absorb. I did this just my unit analysis:

30 000 J/s * (s / 3x10

^{8}m) * (3x10

^{11}m) = 3x10

^{7}J of energy

From these equations, I isolated for wavelength:

E=hf

v=fλ

E/h = v/λ

λ = vh/E

= (3x10

^{8}m/s)(6.63x10

^{-34}J/s) / (3x10

^{7}J)

= 6.63x10

^{-33}m

I have a feeling that it's incorrect to apply E=hf in this situation, because that's a quantization of energy equation -- but otherwise, I don't know how to relate power to wavelength.

So this is obviously wrong. Otherwise, I don't know how to approach this problem. Any help would be great!

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