SME
Grade 11 Science · Problem type
Hydrogen’s spectral lines
Use this for “An electron in hydrogen drops from n = 3 to n = 2. What are the photon’s energy and wavelength?”
Diagram
The electron drops from n = 3 to n = 2 (the Balmer series).
Drawn to scale from n = 2 up; the lower levels are listed below the break.
Photon energy = 13.6 × (1/2² − 1/3²) = 1.889 eV.
Wavelength
=
1240
1.889
=
656
nm:
visible.
This is an example. Type your own values to start a new problem.
E (eV)
=
13.6
eV
×
1
nₗ
2
−
1
nᵤ
2
λ
Wavelength
calculated · nm
Formulas
E
=
13.6
×
(1/
nₗ
2
−
1/
nᵤ
2
)
1.89
=
13.6
×
(
1
2
²
−
1
3
²)
λ
=
1,240
E
656 = 1240/1.89
Assumptions
•
Hydrogen’s levels have energies Eₙ = −13.6/n² eV; the electron can only be on a level.
•
A drop from the upper level to the lower one gives off one photon with the difference in energy.
•
Drops to n = 1 are ultraviolet, to n = 2 visible, to n = 3 infrared. λ = 1240/E nm.
Step-by-step
WE KNOW
nᵤ = 3, nₗ = 2
FIND
photon energy (E), wavelength (λ)
Step 1 · Find photon energy (E)
Use E = 13.6 × (1/nₗ² − 1/nᵤ²)
The photon carries the energy between the two levels.
E
=
13.6
×
(
1
2
²
−
1
3
²)
E
=
13.6
×
(0.25
−
1
9
)
E
=
13.6
×
5
36
E
=
1.89
eV
Step 2 · Find wavelength (λ)
Use λ = 1,240/E
hc = 1240 eV·nm, so the wavelength in nm is 1240 divided by the energy in eV.
λ
=
1240/1.89
λ
=
656
nm
Check
Put the numbers back in. Both sides should match.
1.89
≈
13.6
×
(
1
2
²
−
1
3
²)
✓
656 ≈ 1240/1.89 ✓
← Previous lesson
Modern physics: photons, atomic spectra and relativity
Next lesson →
The photoelectric effect
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
Refresh
Related lessons
Modern physics: photons, atomic spectra and relativity
Main lesson
The photoelectric effect
Use this for “Light of 250 nm falls on a metal with a work function of 2.3 eV. What is the most kinetic energy an electron can leave with? What is the threshold wavelength?”
Moving clocks run slow
Use this for “A spaceship passes at 0.6c. A clock on board ticks 10 s. How long does that take as we see it? How long is the 100 m ship to us?”