Lesson 3: Atomic Spectra & Bohr Model

Lesson at a Glance | He Tirohanga Whakamua

Do NowWhy excited hydrogen gas emits distinct barcode lines instead of a rainbow10 min

Bohr Atomic ModelQuantized energy levels

E_{n}

and transition

Δ E = h f = \frac{h c}{λ}

15 min

Rydberg FormulaCalculating spectral lines for Lyman (

n = 1

), Balmer (

n = 2

), Paschen (

n = 3

)15 min

Portfolio EntryWrite Section 3: Atomic Energy Levels & Spectral Line Analysis10 min

Exit DrillCalculate wavelength of red

H_{α}

line (

n = 3 \to n = 2

)5 min

Ngā Whāinga Ako | Learning Intentions

Students will know

The difference between Continuous, Emission Line, and Absorption Line spectra.
Niels Bohr's quantized model: Electrons exist only in stationary energy orbits ( $E_{n}$ ). Photons are emitted ( $Δ E = E_{i} - E_{f} & g t; 0$ ) or absorbed ( $Δ E = E_{f} - E_{i} & g t; 0$ ) during level jumps.
The Rydberg Formula: $\frac{1}{λ} = R_{H} (\frac{1}{S^{2}} - \frac{1}{L^{2}})$ where $R_{H} = 1.097 \times 10^{7} m^{- 1}$ .

Students will demonstrate

By calculating transition photon energies and matching wavelengths to the visible Balmer series.
By completing Section 3 of their Level 3 Modern Physics Mastery Portfolio.

Do Now | Tīmatanga Whakaaro (10 min)

Atomic Fingerprint Prompt:

"When a high-voltage discharge passes through a tube of hydrogen gas, it glows purple-pink. Viewed through a diffraction grating, why does it split into 4 sharp isolated lines (red, blue-green, blue, violet) rather than a smooth rainbow?"

Unpack: Because electron energy levels inside hydrogen atoms are quantized! Electrons can only occupy fixed orbits ( $n = 1, 2, 3, \dots$ ). Dropping from level $n = 3$ to $n = 2$ releases a photon of exact energy $Δ E = 1.89 eV$ ( $λ = 656 nm$ , red $H_{α}$ line).

Bohr Transitions & Hydrogen Spectral Series (15 min)

1. Energy Level Equation ( $E_{n}$ )

$E_{n} = - \frac{13.6}{n^{2}} eV$
$n = 1$ : Ground state ( $- 13.6 eV$ )
$n = \infty$ : Ionization limit ( $0 eV$ ).

2. Hydrogen Spectral Series

• Lyman Series ( $S = 1$ ): Ultraviolet
• Balmer Series ( $S = 2$ ): Visible light
• Paschen Series ( $S = 3$ ): Infrared.

📁 Physics Modern Portfolio — Section 3: Atomic Spectra & Energy Levels

Students open their Level 3 Physics Portfolio and complete Section 3:

Section 3 Requirements:

1. Energy Level Level Diagram: Draw hydrogen energy levels ( $n = 1$ to $n = 5$ ), illustrating Lyman, Balmer, and Paschen photon emission transitions.

2. Rydberg Wavelength Solver: Use $\frac{1}{λ} = R_{H} (\frac{1}{2^{2}} - \frac{1}{4^{2}})$ to calculate the wavelength of the blue-green $H_{β}$ line ( $n = 4 \to n = 2$ ).

3. Excellence Stellar Absorption Rationale: 1-paragraph explanation of why starlight passing through cooler outer gas clouds produces dark Fraunhofer absorption lines matching stellar emission spectra.

Exit Verification | Ka Mutu Hoki (5 min)

Exit Check:

"My Section 3 uses the Rydberg formula to calculate lambda = 486 nm for the H-beta Balmer line and explains solar Fraunhofer absorption lines."

Teacher Planning & NCEA Alignment

NCEA Level 3 Physics Alignment (3 Credits Internal):

Atomic Spectra: Demonstrate understanding of energy level diagrams, photon emission/absorption, line spectra, and the Rydberg equation.
Bohr Model: Relate quantized angular momentum to discrete atomic stationary states.

Vocabulary: Bohr model, energy level ( $E_{n}$ ), photon emission, absorption, ground state, ionization, Rydberg constant ( $R_{H}$ ), Lyman, Balmer, Paschen.

Other teaching approach: Guided Viewing & Problem Practice →

Lesson 3: Atomic Spectra & Bohr Model of the Atom