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?

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^.