P l a n c k s c h e s W i r k u n g s q u a n t u m : h = 6,626 0693 ( 11 ) × 10 − 34 J s {\displaystyle \mathrm {PlanckschesWirkungsquantum:h=6{,}6260693(11)\times 10^{-34}Js} }
B o l t z m a n n K o n s t a n t e : k = 1,380 6505 ( 24 ) × 10 − 23 J ∘ K − 1 ( p r o G r a d K e l v i n ) {\displaystyle \mathrm {BoltzmannKonstante:k=1{,}3806505(24)\times 10^{-23}J\,^{\circ }K^{-1}\,(pro\,Grad\,Kelvin)} }
L i c h t g e s c h w i n d i g k e i t : c = 3 × 10 8 m s − 1 {\displaystyle \mathrm {Lichtgeschwindigkeit:c=3\times 10^{8}ms^{-1}} }
E i n h e i t U i n W m − 2 n m − 2 ( p r o 1 n m S p e k t r a l b e r e i c h ) : U ( λ , T ) = 2 π h c 2 λ 5 1 e ( h c λ k T ) − 1 {\displaystyle \mathrm {Einheit\,U\,in\,Wm^{-2}nm^{-2}\,(pro\,1\,nm\,Spektralbereich):U(\lambda ,T)={\frac {2\pi hc^{2}}{\lambda ^{5}}}{\frac {1}{e^{\left({\frac {hc}{\lambda kT}}\right)}-1}}} }
U = 2 π ⋅ 6,626 ⋅ 10 − 34 J s ⋅ 9 ⋅ 10 16 m 2 s − 2 ( 5 ⋅ 10 − 7 m ) 5 ⋅ e x p ( 6,626 ⋅ 10 − 34 J s ⋅ 3 ⋅ 10 8 m s − 1 5 ⋅ 10 − 7 m ⋅ 1,380 65 ⋅ 10 − 23 J K − 1 ⋅ 6000 K − 1 ) {\displaystyle \mathrm {U={\frac {2\pi \cdot 6{,}626\cdot 10^{-34}Js\cdot 9\cdot 10^{16}m^{2}s^{-2}}{(5\cdot 10^{-7}m)^{5}\cdot exp({\frac {6{,}626\cdot 10^{-34}J\,s\cdot 3\cdot 10^{8}ms^{-1}}{5\cdot 10^{-7}m\cdot 1{,}38065\cdot 10^{-23}JK^{-1}\cdot 6000K}}-1)}}} }
1 J = 1 k g m 2 s − 2 1 J s = 1 k g m 2 s − 1 1 W = 1 k g m 2 s − 3 {\displaystyle \mathrm {1J=1kgm^{2}s^{-2}\quad 1Js=1kgm^{2}s^{-1}\quad 1W=1kgm^{2}s^{-3}\quad } }
U = 2 π ⋅ 6,626 ⋅ 10 − 34 k g m 2 s − 1 ⋅ 9 ⋅ 10 16 m 2 s − 2 ( 5 ⋅ 10 − 7 m ) 5 ⋅ e x p ( 6.626 ⋅ 10 − 34 k g m 2 s − 1 ⋅ 3 ⋅ 10 8 m s − 1 5 ⋅ 10 − 7 m ⋅ 1.38065 ⋅ 10 − 23 k g m 2 s − 2 K − 1 ⋅ 6000 K ) − 1 {\displaystyle \mathrm {U={\frac {2\pi \cdot 6{,}626\cdot 10^{-34}kgm^{2}s^{-1}\cdot 9\cdot 10^{16}m^{2}s^{-2}}{(5\cdot 10^{-7}m)^{5}\cdot exp({\frac {6.626\cdot 10^{-34}kgm^{2}s^{-1}\cdot 3\cdot 10^{8}ms^{-1}}{5\cdot 10^{-7}m\cdot 1.38065\cdot 10^{-23}kgm^{2}s^{-2}K^{-1}\cdot 6000K}})-1}}} }
U = 374,691 4726 ⋅ 10 − 18 k g m 4 s − 3 ( 5 ⋅ 10 − 7 m ) 5 ⋅ e x p ( 19,878 ⋅ 10 − 26 k g m 3 s − 2 41419 , 5 ⋅ 10 − 30 k g m 3 s − 2 ) − 1 {\displaystyle \mathrm {U={\frac {374{,}6914726\,\cdot 10^{-18}kgm^{4}s^{-3}}{(5\cdot 10^{-7}m)^{5}\cdot exp({\frac {19{,}878\cdot 10^{-26}kgm^{3}s^{-2}}{41419{,}5\cdot 10^{-30}kgm^{3}s^{-2}}})-1}}} }
U = 374,691 4726 ⋅ 10 17 k g m − 1 s − 3 5 5 ⋅ e x p ( 4 , 7991888 ) − 1 {\displaystyle \mathrm {U={\frac {374{,}6914726\,\cdot 10^{17}kgm^{-1}s^{-3}}{5^{5}\cdot exp(4,7991888)-1}}} }
U = 1,199 012712 ⋅ 10 16 k g m − 1 s − 3 120,411 9 = 9,957 5943 ⋅ 10 13 k g m − 1 s − 3 {\displaystyle \mathrm {U={\frac {1{,}199012712\,\cdot 10^{16}kgm^{-1}s^{-3}}{120{,}4119}}=9{,}9575943\,\cdot 10^{13}kgm^{-1}s^{-3}} }
1 k g m − 1 s − 3 k g m 2 s − 3 = 1 W m − 3 = 1 W m − 2 m − 1 ( p r o m S p e k t r a l b e r e i c h ) {\displaystyle \mathrm {1\,{\frac {kgm^{-1}s^{-3}}{kgm^{2}s^{-3}}}=1\,Wm^{-3}=1\,Wm^{-2}m^{-1}\,(\,pro\,m\,Spektralbereich)} }
U = 9,957 5943 ⋅ 10 13 W m − 2 m − 1 ⋅ 10 − 9 = 9,957 5943 ⋅ 10 4 W m − 2 n m − 1 {\displaystyle \mathrm {U=9{,}9575943\,\cdot 10^{13}Wm^{-2}m^{-1}\cdot 10^{-9}=9{,}9575943\,\cdot 10^{4}Wm^{-2}nm^{-1}} }
500nm und K = 6000°[Bearbeiten]
