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13 July, 15:35

A star becomes a red giant and its surface temperature cools from 6000 K to 3000 K. Its peak wavelength originally was 483 nm. What is its peak wavelength after it cools?

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  1. 13 July, 15:41
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    Answer: Peak wavelength

    {lambda max}

    = 9.7*EXP{-7}meter

    Which is approximately,

    1 micro-meter.

    Explanation: lambda{max} which is peak wavelength is inversely proportional to temperature {T}. This is given by the wiens displacement law.

    Lambda max

    =max displacement{Xmax} / T

    For the first case at T = 6000K

    Lambda max = 483 nano-meter

    =483*EXP{-9}meter.

    So let's solve for max displacement {Xmax}.

    Xmax = T*lambda max

    = 6000*483*EXP{-9}

    =2.898*EXP{-3}kelvin-meter

    Xmax would be constant during Temperature change.

    Therefore lambda max at 3000K would be,

    Lambda max

    = {2.898*EXP{-3} K-m} / 3000K

    = 9.7*EXP{-7} meter

    Which is approximately,

    1*EXP{-6} meter = 1 micro-meter

    NOTE: EXP used here means 10^.
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