كيف يحسب الرقم الهيدروجيني pH للمحاليل؟ How to calculate pH and pOH?

يحسب الرقم الهيدروجيني بالعلاقة: pH = -log[H⁺]، وللمحاليل المائية عند 25°C: pH + pOH = 14. إذا كان pH 7 فالمحلول قاعدي. [الصيغة الرمزية الموزونة: pH = -log[H⁺] | pOH = -log[OH⁻] | pH + pOH = 14 | [H⁺][OH⁻] = 10⁻¹⁴]

Theme E — Nuclear and Quantum Physics

E.1.3 Emission and Absorption Spectrum — IB Physics HL Revision Notes & Topical Questions

5 min read 11 parts Lesson 5 of 45 1 quiz

📚 IB Physics HL Hub / Topical Revision

Curriculum Equation Key قوانين الرقم الهيدروجيني والاتزان الأيوني - pH & Acid-Base Equilibrium FormulasFast Exam Solution

pH = -log[H⁺]  |  pOH = -log[OH⁻]  |  pH + pOH = 14  |  [H⁺][OH⁻] = 10⁻¹⁴

Word Equation & Conditions: الرقم الهيدروجيني = -لوغاريتم تركيز أيون الهيدروجين | pH + pOH = 14

Location & Specifications: الاتزان الأيوني، كيمياء 3 ثانوي، التحصيلي، و AP Chemistry.

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Lesson summary

E.1.3 Emission and Absorption Spectrum — IB PHYSICS SL notes: Explain line spectra in terms of discrete atomic energy levels and calculate photon energies of transitions.Continuous spectrum — a hot dense solid such as an incandescent filament emits all wavelengthsEmission line sp…

Emission line spectrum
Unique pattern
Ground state
Negative energies
Allowed changes
Excitation

Part 1 of 9Types of spectrum

Types of spectrum

Continuous spectrum

Continuous spectrum a hot dense solid such as an incandescent filament emits all wavelengths

Emission line spectrum

Emission line spectrum a hot low-pressure gas, such as neon in a sign or sodium in a street lamp, emits only certain wavelengths
They appear as bright coloured lines on a dark background through a grating or prism.

Absorption spectrum

Absorption spectrum white light passed through a cool low-pressure gas has certain wavelengths missing, seen as dark lines on a continuous background

Match

Match the dark lines occur at exactly the same wavelengths as the bright lines of the same element
A hydrogen absorption spectrum is the inverse of its emission spectrum.

Part 2 of 9Spectra as fingerprints

Unique pattern

Unique pattern each element produces its own set of lines, and no two elements share the same set

Use

Use elements in laboratory samples and in stars are identified from their line patterns

Hydrogen

Hydrogen a strong red line at 656 nm

Sodium

Sodium a strong yellow line at 589 nm, giving a yellow flame

Mercury

Mercury most emission lines are below 450 nm, giving a blue light

Lamps

Lamps sodium, mercury and neon are used in street lights and coloured signs

Part 3 of 9Discrete energy levels

Energy levels

Energy levels line spectra show that electrons in atoms have only certain definite energies

Ground state

Ground state the lowest level, with higher levels called excited states

Negative energies

Negative energies energy is measured with the electron at infinite distance as zero, so bound levels are negative
Negative energy only means the electron is bound.

Hydrogen

Hydrogen the ground state is −13.6 eV and the levels follow E_n = −13.6/n² eV

Allowed changes

Allowed changes an electron can change level only by gaining or losing exactly the energy difference between levels

Part 4 of 9Emission of photons

Excitation

Excitation heating a low-pressure gas excites electrons to higher levels
In a discharge tube the atoms are excited by collisions with electrons accelerated by a high voltage.
In a flame, thermal collisions do it.

Emission

Emission when an electron falls from E₂ to E₁, the atom emits one photon with hf = E₂ − E₁
λ = hc/(E₂ − E₁).
h = 6.63 × 10⁻³⁴ J s.

Each transition

Each transition it gives one wavelength and so one spectral line

Large gaps

Large gaps they give high-frequency lines
- (blue or ultraviolet)

Small gaps

Small gaps they give low-frequency lines
- (red or infrared)

Part 5 of 9Absorption of photons

Condition

Condition an electron in E₁ absorbs a photon only if its energy equals the gap to a higher level

Other photons

Other photons they pass through, so specific wavelengths are removed from the beam

Dark lines

Dark lines absorbed energy is re-emitted in random directions, so the intensity in the original direction is reduced

Part 6 of 9Ionisation

Ionisation energy

Ionisation energy the energy needed to remove an electron from the ground state completely, 13.6 eV for hydrogen

Excess energy

Excess energy a photon or collision with more energy than this ionises the atom, and the excess becomes kinetic energy of the freed electron

Spectrum

Spectrum the ionising spectrum is continuous because the ejected electron may have any kinetic energy

Part 7 of 9Spectra of stars

Sun's spectrum

Sun's spectrum its surface gives a continuous spectrum crossed by dark Fraunhofer lines from gases in the cooler outer atmosphere

Identification

Identification comparing line positions with laboratory spectra identifies the elements present
Helium was first discovered in the Sun this way.

Red shift

Red shift lines shifted to longer wavelengths show a star moving away from us

Wavelength measurement

Wavelength measurement a diffraction grating, d sin θ = nλ, measures wavelengths and so energy-level differences
What the symbols mean: d = grating spacing (m) · θ = angle of the nth-order maximum · n = order number (0, 1, 2 …) · λ = wavelength (m)

Part 8 of 9Energy level diagrams

Layout

Layout levels are horizontal lines at heights proportional to energy, with vertical arrows for transitions
Longer arrows mean higher-frequency photons.

Number of lines

N levels allow N(N − 1)/2 lines if all transitions are allowed, so four levels give six lines

Method

Method find the differences between pairs of levels and convert each to a wavelength with λ = hc/ΔE
hc = 1.99 × 10⁻²⁵ J m or 1240 eV nm.

Units

Units convert eV to joules (1 eV = 1.60 × 10⁻¹⁹ J) before using hf = E with SI values

Part 9 of 9More from the specification

Rutherford Alpha Particle Scattering Experiment

Bombarding thin gold foil with energetic alpha particles revealed that most particles pass straight through without deflection,
while a small fraction deflect through angles greater than 90°.

Discovery of the Atomic Nucleus

Rutherford's scattering observations demonstrated that the atom consists mostly of empty space, with virtually all positive charge and mass concentrated in a tiny central nucleus.

Atomic Emission Spectra and Energy Levels

When excited atomic electrons transition between quantised energy levels, photons of discrete frequencies are emitted according to the Planck-Einstein equation ΔE = h f = h c / λ.

Atomic Absorption Spectra

Passing continuous white light through a cool gas produces dark absorption lines at specific wavelengths, matching the photon energies absorbed by electrons transitioning to higher energy states.

Rutherford Alpha Particle Scattering Experiment

Bombarding thin gold foil with energetic alpha particles revealed that most particles pass straight through without deflection,
while a small fraction deflect through angles greater than 90°.

Discovery of the Atomic Nucleus

Rutherford's scattering observations demonstrated that the atom consists mostly of empty space, with virtually all positive charge and mass concentrated in a tiny central nucleus.

Atomic Emission Spectra and Energy Levels

When excited atomic electrons transition between quantised energy levels, photons of discrete frequencies are emitted according to the Planck-Einstein equation ΔE = h f = h c / λ.

Atomic Absorption Spectra

Passing continuous white light through a cool gas produces dark absorption lines at specific wavelengths, matching the photon energies absorbed by electrons transitioning to higher energy states.

Nucleus

Small, dense, positively charged centre of the atom.

Scattering

Deflection of particles from their original path.

Alpha particle

Helium nucleus, charge +2.

Nuclear notation

Symbol showing mass number and atomic number.

Rutherford scattering

Scattering of charged particles by a nucleus through electrostatic repulsion alone.

Subatomic particle

A particle smaller than an atom, e.g. the electron.

Key terms

Term	Meaning
Line spectrum	Spectrum with only certain wavelengths, characteristic of the element.
Energy level	Allowed energy of a bound electron in an atom.
Ground state	Lowest energy level of an atom.
Ionisation energy	Energy needed to remove an electron from the ground state.
Absorption spectrum	Dark lines on a continuous background from gas absorbing photons.
Photon	A quantum of electromagnetic radiation with energy hf.

Avoid these mistakes

Thinking a photon of any energy can be absorbed — only photons matching an energy gap, or exceeding the ionisation energy, are absorbed.

Confusing the spectra — emission lines are bright on a dark background and absorption lines are dark on a continuous spectrum.

Taking negative energies to mean the electron has less than zero energy in a physical sense — it only means the electron is bound.

Forgetting to convert eV to joules before using hf = E with SI values.

Believing the spectrum of a hot dense solid is a line spectrum — it is continuous.

Last updated: 15 October 2026