Energiebilanz für emittiertes oder absorbiertes Licht
Δ E = E n − E m {\displaystyle \Delta E=E_{n}-E_{m}\,} Δ E = h ⋅ f {\displaystyle \Delta E=h\cdot f}
E n , E m {\displaystyle E_{n},E_{m}} = Energieniveaus des Atoms f {\displaystyle f} = Frequenz des Lichtes h {\displaystyle h} = Planck-Konstante h = 6,626 08 ⋅ 10 − 34 k g ⋅ m 2 s {\displaystyle h=6{,}62608\cdot 10^{-34}{\frac {\mathrm {kg} \cdot \mathrm {m} ^{2}}{\mathrm {s} }}}
Spektralserien des Wasserstoffatoms
1 λ = R H ⋅ ( 1 n 2 − 1 m 2 ) {\displaystyle {\frac {1}{\lambda }}=R_{H}\cdot \left({\frac {1}{n^{2}}}-{\frac {1}{m^{2}}}\right)} f = R y ⋅ ( 1 n 2 − 1 m 2 ) | n < m {\displaystyle f=R_{y}\cdot \left({\frac {1}{n^{2}}}-{\frac {1}{m^{2}}}\right)\qquad |n<m}
λ {\displaystyle \lambda \,} = Wellenlänge R H {\displaystyle R_{H}} = Rydberg-Konstante
R H = 1,097 37315 ⋅ 10 7 m − 1 {\displaystyle R_{H}=1{,}09737315\cdot 10^{7}\mathrm {m} ^{-1}} R y {\displaystyle R_{y}\,} = Rydberg-Frequenz R y = 3,289 84195 ⋅ 10 15 H z {\displaystyle R_{y}=3{,}28984195\cdot 10^{15}\mathrm {Hz} }
Relative Atommasse
A r = m A u {\displaystyle A_{\mathrm {r} }={\frac {m_{\mathrm {A} }}{\mathrm {u} }}}
m A {\displaystyle m_{\mathrm {A} }} = Masse des Atoms
u = atomare Masseneinheit 1 u = 1,660 540 ⋅ 10 − 27 k g {\displaystyle 1\,\mathrm {u} =1{,}660540\cdot 10^{-27}\,\mathrm {kg} }
Nukleonenzahl (Massenzahl)
A = Z + N {\displaystyle A=Z+N}
X {\displaystyle X} = Symbol des Elements Z {\displaystyle Z} = Protonenzahl (Kernladungszahl, Ordnungszahl im Periodensystem) A {\displaystyle A} = Massenzahl N {\displaystyle N} = Neutronenzahl m p {\displaystyle m_{p}} = Masse eines Protons m p = 1,672 6231 ⋅ 10 − 27 k g {\displaystyle m_{p}=1{,}6726231\cdot 10^{-27}\,\mathrm {kg} } m n {\displaystyle m_{n}} = Masse eines Neutrons m n = 1,674 9286 ⋅ 10 − 27 k g {\displaystyle m_{n}=1{,}6749286\cdot 10^{-27}\,\mathrm {kg} } c {\displaystyle c} = Lichtgeschwindigkeit im Vakuumc = 2,997 92458 ⋅ 10 8 m s {\displaystyle c=2{,}99792458\cdot 10^{8}{\frac {\mathrm {m} }{\mathrm {s} }}}
Symbolschreibweise
Z A X {\displaystyle {}_{Z}^{A}X}
Kernmasse m K {\displaystyle m_{\mathrm {K} }} und Massendefekt Δ m {\displaystyle \Delta m}
m K < Z ⋅ m p + N ⋅ m n {\displaystyle m_{\mathrm {K} }<Z\cdot m_{p}+N\cdot m_{n}} Δ m = ( Z ⋅ m p + N ⋅ m n ) − m K {\displaystyle \Delta m=\left(Z\cdot m_{p}+N\cdot m_{n}\right)-m_{\mathrm {K} }}
Kernbindungsenergie
E B = Δ m ⋅ c 2 {\displaystyle E_{\mathrm {B} }=\Delta m\cdot c^{2}}