Astar 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?

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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answer: the metamorphic rocks are formed when they are exposed to high pressure and high temperatures. this happens when one of the earth's plates comes in contact with the other plate by traveling in opposite directions, straight into each other or slipping under one another. the friction that is caused by this activity results in   melting of rocks and when it cools they are known as metamorphic rocks. this process needs a controlled amount of pressure and temperature otherwise it may turn into magma.