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.1.6 Deviations from Rutherford Scattering — IB Physics HL Revision Notes & Topical Questions

5 min read 9 parts Lesson 8 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.1.6 Deviations from Rutherford Scattering — IB PHYSICS HL notes: Explain why high-energy alpha particles deviate from Rutherford scattering and what this shows about the strong force, nuclear size and quarks.Assumption — only electrostatic repulsion between point charges acts, …

Prediction
Observation
Range of the strong force
Closest approach
Electric force
Greatest deviation

Part 1 of 7What Rutherford predicted

Assumption

Assumption only electrostatic repulsion between point charges acts, and the target nucleus stays fixed

Prediction

Prediction as the scattering angle increases, the number of alpha particles scattered decreases

Agreement

Agreement found correct at low to moderately high energies for alpha particles of a few MeV on gold

Failure

Failure the prediction fails if the projectile gets close enough to feel other forces or the target recoils

Part 2 of 7Deviations at high energy

1Energy

Energy above about 27.5 MeV significant deviations are observed

2Observation

Observation the number of back-scattered alpha particles falls sharply to zero instead of following the expected rate

3Cause

Cause the alpha particles come close enough to the nucleons to feel the strong nuclear force

4Range of the strong force

Range of the strong force significant below about 1.5 fm and acting over roughly 1–3 fm

5Evidence

Evidence deviations provide evidence for the strong nuclear force

6Closest approach

Closest approach it becomes comparable to the nuclear radius

Part 3 of 7Effect of the target nucleus

Electric force

F = kqQ/r², so a nucleus with smaller charge lets the alpha particle approach closer at the same energy

Gold

Z = 79

Aluminium

Z = 13, so alpha particles get closer and more deviation is seen

Greatest deviation

Greatest deviation high alpha energy and target nuclei of low nucleon number

Light targets

Light targets if the target is as light as the alpha particle, it recoils, so scattering angles differ from the fixed-target calculation

Part 4 of 7Electron diffraction and nuclear size

Electrons as probes

Electrons as probes they do not feel the strong force and interact only electromagnetically and weakly

Wavelength

λ = h/p can be smaller than a nucleus at high energy

Pattern

Pattern scattered intensity shows diffraction with a first minimum that gives the nuclear radius

Charge distribution

Charge distribution electron scattering probes the nuclear charge distribution

Part 5 of 7Deep inelastic scattering

1Higher energy electrons

Higher energy electrons many GeV electrons on protons deviate from point-like scattering

2Result

Result there are small hard point-like centres inside the proton

3Charges

Charges the centres have fractional charge

4Conclusion

Conclusion protons and neutrons contain quarks

5First done

First done at Stanford in the late 1960s

Part 6 of 7What each probe shows

Projectile	What deviation shows
Alpha particles	The strong force and the range of nuclear forces
Electrons	The charge distribution and radius of the nucleus
Very high-energy electrons	The internal structure of nucleons

Part 7 of 7More from the specification

Alpha trajectory around nuclear orbit

Alpha trajectory around nuclear orbit high-energy alpha particles penetrating close nuclear distances deviate from Rutherford scattering, escaping classical Coulomb scattering orbit.

Deviations from Rutherford Scattering

At extremely high alpha particle energies, particles penetrate close enough to the gold nucleus to experience the attractive strong nuclear force,
causing deviations from pure Coulomb scattering predictions.

Hydrogen Spectral Series

Electron transitions down to the n=1 ground state produce the ultraviolet Lyman series, transitions to n=2 produce the visible Balmer series,
and transitions to n=3 yield the infrared Paschen spectrum.

The Rydberg Equation

The wavelengths of emission photons from atomic hydrogen are calculated using the Rydberg equation: 1 / λ = R_H * (1/n₁² - 1/n₂²),
where R_H is the Rydberg constant.

Quantization of Photons and Energy Levels

Absorption spectra are produced when cold atomic gas absorbs photons whose energy precisely matches the difference between atomic levels, leaving distinct dark absorption lines on a continuous spectrum.

Angular momentum

L = Iω for a rigid body; L = mvr_⊥ for a particle.

Emission spectrum

The set of discrete wavelengths emitted by excited atoms of an element.

Photon

A quantum of electromagnetic energy, E = hf

Spectrum

Range of colours in white light.

Constant

Not changing.

Momentum

P = mv, a vector.

Density

Mass per unit volume.

Absorption

The conversion of wave energy to internal energy of the medium.

Energy level

A discrete energy an electron in an atom can have

Photon energy

E = hf = hc/λ, the energy carried by one photon.

∆E

∆E hf = E2 − E1

What the symbols mean: E = energy of one photon (J) · h = Planck constant (6.63 × 10⁻³⁴ J s) · f = frequency (Hz)

Key terms

Term	Meaning
Strong nuclear force	The short-range attractive force between nucleons.
Rutherford scattering	Scattering of charged particles by a nucleus through electrostatic repulsion alone.
Deep inelastic scattering	Scattering of very high-energy electrons by nucleons that revealed quarks.
Electron diffraction	Diffraction of electrons used to measure nuclear radius.
Quark	A fundamental particle that makes up protons and neutrons.

Avoid these mistakes

Saying the deviation shows Coulomb's law fails — other forces, the strong force, come into play.

Using electrons to explain the strong force — electrons do not feel it.

Forgetting that Rutherford scattering assumes a heavy fixed target.

Thinking deviations appear at low energies — they appear when the particle gets close at high energy.

Confusing electron diffraction with alpha scattering — electrons probe charge distribution and alphas probe the force range.

Last updated: 15 October 2026