In lectures you will derive the well known formula for the energy levels of a hydrogen atom: En = m²e4 1 2 (4πεo)² ħ² n² = -Ry 1 (1) where 'n' is the principal quantum number and 'Ry' is the Rydberg unit of energy, Ry= 13.6 eV. The energy of a photon emitted by an excited hydrogen atom corresponds to the difference between the energy of the initial and final state. The emission lines of hydrogen are grouped according to the energy level the electron transitions to. For example an electron making a transition to the n = 1 level is classified into the Lyman series, n = the Balmer series, n = 3 the Paschen series, etc. = 2 Question 2: For a particular series 'f', formulate an expression for the wavelength '2 (n)' of the photon emitted in a transition from the higher energy state 'n'. Tabulate the first seven emission lines of the Balmer series to the nearest nm.
In lectures you will derive the well known formula for the energy levels of a hydrogen atom: En = m²e4 1 2 (4πεo)² ħ² n² = -Ry 1 (1) where 'n' is the principal quantum number and 'Ry' is the Rydberg unit of energy, Ry= 13.6 eV. The energy of a photon emitted by an excited hydrogen atom corresponds to the difference between the energy of the initial and final state. The emission lines of hydrogen are grouped according to the energy level the electron transitions to. For example an electron making a transition to the n = 1 level is classified into the Lyman series, n = the Balmer series, n = 3 the Paschen series, etc. = 2 Question 2: For a particular series 'f', formulate an expression for the wavelength '2 (n)' of the photon emitted in a transition from the higher energy state 'n'. Tabulate the first seven emission lines of the Balmer series to the nearest nm.
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Transcribed Image Text:3.2 Emission Lines
In lectures you will derive the well known formula for the energy levels of a hydrogen
atom:
En =
m²e4 1
2 (4πεo)² ħ² n²
1
n²
= -Ry
(1)
where 'n' is the principal quantum number and 'Ry' is the Rydberg unit of energy, Ry=
13.6 eV. The energy of a photon emitted by an excited hydrogen atom corresponds to the
difference between the energy of the initial and final state. The emission lines of hydrogen
are grouped according to the energy level the electron transitions to. For example an
electron making a transition to the n = 1 level is classified into the Lyman series, n = 2
the Balmer series, n = 3 the Paschen series, etc.
Question 2: For a particular series 'f', formulate an expression for the wavelength
'λ (n)' of the photon emitted a transition from the higher energy state 'n'.
Tabulate the first seven emission lines of the Balmer series to the nearest nm.
3.3 Transition rules
The energy levels of the Hydrogen atom are determined by 'n' as the orbitals 'l' are de-
generate. The emission of a photon requires that Al = ±1 to conserve angular momentum.
Therefore the first line of the Lyman series (n = 2 → 1) is a transition from 2p → 1s, as
2s →→ 1s is a forbidden transition for single photon emission.
Question 3: For the first line of the Balmer series determine the possible transi-
tions involving a photon. Use the form in the previous paragraph, ie. nl → n'l'.
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