Physics help! Wien Law?

Question

1. What is the peak wavelength of a blackbody at a temperature of 325 K?


2. A star is observed to have a peak intensity per unit wavelength at 455.0 nm. What is the surface temperature of the star?

Answer 1

Wein's law can be stated as follows:

lambda*T = C3



where C3 is a fundamental constant, lambda is the peak vacuum wavelength, and T is the temperature in Kelvin.



For problem 1, it is re-arranged as lambda = C3/T



For problem 2, it is re-arranged as T = C3/lambda



Data problem 1:

T:=325 K; C3:=2898 µm-Kelvin;



Data problem 2:

lambda:=0.4550 µm; C3:=2898 µm-Kelvin;



Results:

problem 1: lambda = 8.917 µm

problem 2: T = 6369 Kelvin

Answer 2

Wien's Law says that



L(max)* T = constant



Where L(max) is peak wavelength (m) and T is temperature (K)



I believe this constant is about 2.98*10^-3 K m (not to be confused with millikelvin! or kilometres)



Remember that 1m = 10^9nm

Answer 3

lambda peak = b/T with T the temperature in Kelvin and b = 2,897,768 nm*K (nm = nanometer)

So here 1/ peakwl = 8.9 micron (a very flat peak, though) and 2/ T = 6369 K