E.1 Concept Builder Part 2 · HL Physics Notebook

1. Start with predictions

7 minPairs

ATL Thinking: predict and justify. Social: compare with a partner. You will test every prediction later with a simulation.

1.1Hydrogen gas at low pressure glows when a current passes through it. You look at the light through a diffraction grating. You see…

A. a full rainbow (a continuous spectrum) B. a few bright lines of particular colours C. a rainbow with dark lines

You test it in stage 2.

1.2In hydrogen, which transition gives the photon with the LONGER wavelength?

A. n = 3 → n = 2 B. n = 4 → n = 2 C. both give the same wavelength

You test it in stage 3.

1.3White light passes through cool hydrogen gas. The spectrum of the light that comes through has dark lines. These dark lines are at…

A. the same wavelengths as the bright lines of hydrogen’s emission spectrum B. different wavelengths from the bright lines C. random wavelengths that change each time

You test it in stage 4.

1.4A hydrogen atom is in its ground state (−13.6 eV). A photon of energy 11.0 eV meets it. What happens?

A. the photon gives 10.2 eV to the atom and leaves with 0.8 eV B. the photon is not absorbed C. the atom is ionised

You test it in stage 5.

1.5Explain the reasons for one of your predictions.

What a good answer looks like

A good reason uses an idea, for example: “The atom can only have certain energies, so…” or “A bigger energy gap means…”. You will see in the simulations which reasons hold.

2. Emission spectra: test prediction 1.1

17 minPairs → individual

ATL Research: link an observation to a model. Self-management: convert units carefully.

Simulation A · Glowing hydrogen choose a transition; each photon adds its line to the spectrum below

from level n = 3to level n = 2

photon energy ΔE—

wavelength λ—

region—

Photon energy E = hf = hc/λE_photon = ΔE = E_upper − E_lower h = 6.63 × 10⁻³⁴ J s, c = 3.00 × 10⁸ m s⁻¹, 1 eV = 1.60 × 10⁻¹⁹ J. Hydrogen levels: −13.6, −3.40, −1.51, −0.85, −0.54, −0.38 eV.

2.1Transition n = 3 → n = 2. Photon energy in eV, ΔE =

eV

2.2The same photon energy in joules =

J

2.3Wavelength of this photon, λ =

m

Back check

2.bBack check: the frequency of this photon, f =

Hz

2.4Press “Show every line”. Why does hydrogen give only a few lines and not a full rainbow?

the atom can only have certain energies, so only certain energy differences, and so only certain wavelengths, are possible the grating blocks the other colours hydrogen is too cold to glow in every colour

From a transition to a wavelength

Find the gap: ΔE = E_upper − E_lower (in eV).
Change to joules: × 1.60 × 10⁻¹⁹.
λ = hc/ΔE (hc = 1.99 × 10⁻²⁵ J m). Quick check: λ in nm ≈ 1240/ΔE in eV.

Find the mistake

A student finds the wavelength for a gap of 1.89 eV:

λ = hc/E = 1.99 × 10⁻²⁵/1.89 = 1.05 × 10⁻²⁵ m

What is wrong?

The energy must be in joules: λ = 1.99 × 10⁻²⁵/(1.89 × 1.60 × 10⁻¹⁹) = 6.58 × 10⁻⁷ m. It should be λ = E/hc. Nothing is wrong.

Hinge question

Choose your answer. You will see at once if it is right, and why.

Electrons in hydrogen atoms are excited to n = 4. As they fall back (by any route), how many different spectral lines can appear?

A. 3 B. 4 C. 6

2.5Was prediction 1.1 right? Explain with energy levels.

What a good answer looks like

B, a few bright lines. An electron falling from one level to a lower one gives one photon of energy ΔE = hc/λ. The atom has only certain energy levels (−13.6, −3.40, −1.51 eV …), so only certain values of ΔE and only certain wavelengths appear, such as 658 nm for n = 3 → 2. A continuous spectrum would need every energy to be possible.

3. Energy-level diagrams: test prediction 1.2

16 minPairs → individual

ATL Thinking: one rule for many questions. Communication: explain with the gap, not the arrow length.

Simulation B · Read an energy-level diagram an atom with four levels: E₁ = −12.0 eV, E₂ = −6.5 eV, E₃ = −3.6 eV, E₄ = −1.8 eV

energy gap ΔE—

wavelength λ—

region—

One rule bigger ΔE → higher f → shorter λ E = hf, so f ∝ ΔE. E = hc/λ, so λ ∝ 1/ΔE. The longest arrow gives the shortest wavelength.

3.1Choose 4 → 3. Wavelength, in nm =

nm

3.2Choose 3 → 2. Wavelength, in nm =

nm

3.3Which transition gives the SHORTEST wavelength?

4 → 1 4 → 3 2 → 1

3.4Try all six. Which lines are visible (400 nm to 700 nm)?

only 4 → 3 and 3 → 2 all six only 2 → 1

Find the mistake

A student answers “Which arrow gives the longest wavelength?”:

“4 → 1, because it is the longest arrow.”

What is wrong?

It is the other way round: the longest arrow is the biggest energy, so the SHORTEST wavelength. The longest wavelength is the smallest gap, 4 → 3. All arrows give the same wavelength. Nothing is wrong.

What if? · stretch

3.wAnother atom: E₁ → E₀ gives 600 nm and E₂ → E₀ gives 400 nm. The wavelength for E₂ → E₁, in nm =

nm

Hinge question

Choose your answer. You will see at once if it is right, and why.

An atom has 5 energy levels. How many different lines can its emission spectrum have?

A. 5 B. 10 C. 15

3.5Was prediction 1.2 right? Explain with the energy gaps.

What a good answer looks like

A, n = 3 → 2. Its gap is 1.89 eV, smaller than the 2.55 eV gap of n = 4 → 2. Since λ = hc/ΔE, the smaller gap gives the longer wavelength: 658 nm (red) against 488 nm (blue-green).

4. Absorption spectra: test prediction 1.3

15 minPairs → individual

ATL Thinking: compare two observations of the same process. Communication: use the three marking points.

Simulation C · White light through a cool gas look along the beam, or from the side

you see—

line wavelengths—

why—

Absorption spectrum: a continuous spectrum with dark lines at the wavelengths absorbed by an element. Emission spectrum: the set of wavelengths emitted by an element (bright lines on a dark background). Every element has its own lines: they show the chemical composition.

4.1Choose hydrogen. Compare “along the beam” with “from the side”. The dark lines and the bright lines are at…

exactly the same wavelengths different wavelengths the dark lines are all in the red

4.2A dark line of hydrogen is at 488 nm. Energy of the absorbed photon, in eV =

eV

Back check

4.bBack check with the quick rule: 1240/2.55 =

nm

4.3Choose helium. What does this show?

each element has its own set of lines, so the lines tell us which elements are in a gas or a star helium and hydrogen have the same lines the lines tell us the mass of the nucleus

Find the mistake

A student explains the dark lines:

“The cool gas absorbs these photons and keeps the energy, so these wavelengths are missing.”

What is wrong?

The excited atoms quickly emit photons of the same wavelengths again, but in ALL directions, so very few go along the original beam. That is why the lines are dark. The gas reflects these photons back to the lamp. Nothing is wrong.

“Explain the formation of an absorption spectrum” (3 marks)

White light (a continuous spectrum) passes through a cool gas.
Photons with energy equal to the difference between two energy levels are absorbed, and electrons move to higher levels (E = hf = ΔE).
The photons are re-emitted in all directions, so these wavelengths are missing (dark lines) in the transmitted light.

Hinge question

Choose your answer. You will see at once if it is right, and why.

What do the lines of a spectrum tell us about a star?

A. which elements it contains (its chemical composition) B. the structure of its nuclei C. how much mass is changed into energy

4.4Was prediction 1.3 right? Explain with energy levels.

What a good answer looks like

A, the same wavelengths. A photon is absorbed only if its energy equals the gap between two levels, and the photons in the emission spectrum come from exactly the same gaps (E = hc/λ). So hydrogen absorbs at 658, 488, 435 and 412 nm, the same wavelengths it emits. The lines look dark because the absorbed energy is re-emitted in all directions.

5. Excite or ionise? Test prediction 1.4

15 minIndividual

ATL Thinking: compare two processes. Self-management: learn definitions word for word.

Simulation D · Excite or ionise? a hydrogen atom in its ground state meets a photon or an electron

energy of the photon or electron 11.0 eV

what happens—

atom ends in—

energy left over—

Photon: absorbed only if its energy equals a gap (all or nothing). Electron: can give the atom part of its kinetic energy (exactly one gap) and keep the rest. Ionisation energy: the minimum energy needed to remove an electron from an atom in its ground state (hydrogen: 13.6 eV).

5.1Choose “photon” and 11.0 eV. What happens?

nothing: the photon passes through the atom goes to n = 2 and the photon keeps 0.8 eV the atom is ionised

5.2Choose “electron” and 11.0 eV. The kinetic energy the electron keeps =

eV

5.3A photon of 14.0 eV meets the atom. Kinetic energy of the freed electron =

eV

5.4An atom is in the state n = 2 (−3.40 eV). The energy needed to ionise it =

eV

What if? · stretch

5.wThe minimum frequency of a photon that can ionise an atom in n = 2, f =

Hz

Find the mistake

A student answers prediction 1.4:

“The atom takes 10.2 eV and goes to n = 2; the photon carries on with 0.8 eV.”

What is wrong?

A photon is absorbed completely or not at all. Only an ELECTRON can give part of its energy. An 11.0 eV photon is not absorbed. The atom would go to n = 3. Nothing is wrong.

Hinge question

Choose your answer. You will see at once if it is right, and why.

Which definition earns the mark for “ionisation energy”?

A. the minimum energy needed to remove an electron from an atom in its ground state B. the energy of the electron in the atom C. the energy needed to move an electron up one level

5.5Was prediction 1.4 right? Explain.

What a good answer looks like

B, the photon is not absorbed. A photon is absorbed only if its energy equals the gap between two levels exactly, because the whole photon is taken or none of it. From the ground state the gaps are 10.20, 12.09, 12.75 eV …; none is 11.0 eV, and 11.0 eV is less than the 13.6 eV needed to ionise. (An electron of 11.0 eV, however, could excite the atom to n = 2 and keep 0.8 eV.)

6. Show it, then reflect

10 minIndividual

ATL Communication + Self-management: choose how to show your understanding, retrieve without notes, plan your next step.

Success criteria: your answer must…

say that the energy levels are discrete;
use E = hf = hc/λ with ΔE in joules;
say that a bigger gap gives a shorter wavelength;
use one number from a simulation today.

Option A · Written

One paragraph: “Why line spectra are evidence for discrete energy levels, and why absorption lines are dark.”

Option B · Sketch

Draw four energy levels with the six transitions; label the longest and the shortest wavelength and say which are visible.

Option C · Spoken

Explain to your partner in 1 minute what a hydrogen atom does with an 11.0 eV photon and with an 11.0 eV electron. Your partner ticks the success criteria.

6.1Write your paragraph or your notes.

What a good answer looks like

Model answer (Option A): A glowing gas gives only a few bright lines. Each line has one wavelength and so one photon energy (E = hc/λ), and each photon is emitted when an electron falls between two energy levels (E = ΔE). If an atom could have any energy, we would see a continuous spectrum, so the energy levels must be discrete: for hydrogen, n = 3 → 2 gives 1.89 eV and 658 nm. When white light passes through a cool gas, photons with energies equal to these gaps are absorbed and the electrons move up. The atoms re-emit the photons in all directions, so very few continue along the beam: the same wavelengths appear as dark lines.

Exit ticket (no notes)

1An electron falls from −0.85 eV to −3.40 eV. Photon energy, in eV =

2A photon has an energy of 3.0 × 10⁻¹⁹ J. In eV =

3The biggest energy gap in an energy-level diagram gives the photon with the…

longest wavelength shortest wavelength lowest frequency

4A photon of 10.2 eV meets a hydrogen atom in its ground state. The photon…

is absorbed and the atom goes to n = 2 passes through ionises the atom

5Electrons are excited to n = 4. How many different lines can be emitted as they fall back?

6Which idea from today is still the least clear to you?

What a good answer looks like

There is no single right answer. A good answer names one idea exactly, for example: “I am not sure when a photon is absorbed and when an electron can excite an atom.”

7Feedforward: Next time I will check ________ before I ________.

What a good answer looks like

A good feedforward names an action: “Next time I will change eV to joules before I use λ = hc/E.”

TOK · 2 minutes

Theory of knowledge: how do we know? There is no single right answer. Write two or three sentences.

TOKWe know which elements are in stars thousands of light years away only from the lines in their light. How far can we trust knowledge that comes entirely from instruments and from a model of the atom?

Points you could make

The method is tested on Earth first: the lines of every element are measured in the laboratory and they never change.
Independent checks agree, for example helium was found in the Sun’s spectrum and later on Earth with the same lines.
The knowledge depends on assumptions (the same physics everywhere in the universe) that cannot be tested directly, so it is very reliable but not certain.

Read the notes Part 3 (HL) Back to E.1

Spectra, energy levels and photons

Learning goals: by the end you can…

1. Start with predictions

2. Emission spectra: test prediction 1.1

3. Energy-level diagrams: test prediction 1.2

4. Absorption spectra: test prediction 1.3

5. Excite or ionise? Test prediction 1.4

6. Show it, then reflect

Exit ticket (no notes)