FE Physics

Formulas & Explanation

Formulas & Explanation

Dutch version

**
Line spectra**

Atoms of a low-pressure gas can
occur in certain energy states. The lowest energy state
**E _{1}**

Higher energy levels are the 1e, 2 e, ….. exited states.
**E _{2} ,E_{3}**
enz

The energy levels of the H-atom are :

**
E∞**
= 0.0 eV
ionized state

--------------

**
E _{3}**
= -1.5
eV
2

**
E _{2}**
= -3.4
eV
1

**
E _{1}**
= - 13.6 eV
groundstate

Remark: between the 2^{e} excited state and the ionized state are many
more energy levels.

Whenever a atom falls back to a lower energy level the surplus energy is
releases as a photon.

*
Example*

A H-atom is in the 2^{e} excited state.

The atom falls back to the ground state.

There are 2 posibilities:

1.
Direct from E_{3} to E_{1}
(ΔE
=E_{3}- E_{1}=-1.5- -13.6 = 12.1 eV)

2.
From E_{3} to E_{2} (ΔE
= -1.5- - 3.4 = 1.9 eV ) . Then follows
E_{2} to E_{1}

(- 3.4 - - 13.6 = 10.2 eV)

*
Calculate the wavelength corresponding the transition of 1.9 eV
(E3→E2)*

ΔE
= 1.9 eV = 1.9 x 1.6 x 10^{-19 }= 3.04 x 10^{-19} J

**
ΔE=h
f**
3.04 x 10^{-19 }= 6.63 x 10^{-34 }. f
f=3.04 x 10^{-19 }/ 6.63 x 10^{-34} = 4.59 x 10^{14
}Hz

**
**

**
c = f λ
**
3.00 x 10^{8 }= 4.59 x 10^{14
}.λ
λ
= 3.00 x 10^{8} /4.59 x 10^{14 }= 6.54 x 10^{-7} m = 654
nm

This is the red line of the H-spectrum.