Solving for temperature using Wiens Law

1. The problem statement, all variables and given/known data

A blackbody has a peak wavelength of 2x10^-6m , use the wavelength form of Wiens Law to calculate its temperature

2. Relevant equations
[tex]
\lambda_{peak}=\frac{hc}{5kT} \\
I_{\lambda}=\frac{2hc^2}{\lambda^5(e^{hc/ \lambda kT}-1)}
[/tex]


3. The attempt at a solution
I was not sure what equation to use but from the lecture booklet the two above are the only ones with temperature in them, the second one doesnt give me enough information as I dont know [itex]I_{\lambda}[/itex], however my answer just doesnt seem correct to me.

[tex]
\lambda_{peak}=\frac{hc}{5kT} \\
2×10^{-6}=\frac{(6.626×10^{-34})(2.997×10^8)}{5(1.38×10^{-23})T} \\
2×10^{-6}=\frac{1.986×10^{-25}}{(6.98×10^{-23})T} \\
T(6.98×10^{-23})(2×10^{-6})=1.986×10^{-25} \\
T(1.396×10^{-28})=1.986×10^{-25} \\
T=\frac{1.986×10^{-25}}{1.396×10^{-28}}=1422K
[/tex]

 

Ah, I think so yeah but there is no K on the top though, it is given as

[tex]
\lambda_{peak}=\frac{2.898×10^{-3}}{T}
[/tex]

Using that I get

[tex]
T=\frac{2.898×10^{-3}}{2×10^{-6}}= 1449 Kelvin\\
[/tex]

So it is roughly the same, so the previous answer must have been correct :) Thanks.

EDIT: Wow I have made some silly input errors today :)

 

Ah right, sorry :)