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.3 Radioactive Decay — IB Physics HL Revision Notes & Topical Questions

10 min read 13 parts Lesson 17 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.3 Radioactive Decay — IB PHYSICS HL notes: Describe isotopes, radioactive decay and its radiations, decay equations, activity, half-life and the decay law, applications, binding energy, nuclear stability, energy levels and the neutrino.Isotopes — nuclei with the same number of …

Isotopic data
Carbon dating
Spontaneous
Evidence of randomness
Definition
Natural sources

Part 1 of 10Isotopes and the nature of decay

Isotopes

Isotopes nuclei with the same number of protons but different numbers of neutrons
Z is fixed and A differs, as in hydrogen, deuterium and tritium

Isotopic data

Isotopic data the relative amounts of the isotopes in a substance
Relative atomic mass is the abundance-weighted average, found with a mass spectrometer

Carbon dating

Carbon dating compares the ratio of carbon-12 to carbon-14 with the ratio in living tissue

Radioactive decay

Radioactive decay the spontaneous disintegration of a nucleus to form a more stable nucleus, emitting an alpha, beta or gamma particle

Spontaneous

Spontaneous it cannot be influenced by temperature, pressure or chemical conditions

Random

Random the exact time of decay of a nucleus cannot be predicted, but each nucleus has a constant probability of decaying per unit time

Evidence of randomness

Evidence of randomness irregular, unpredictable counts on a Geiger–Müller tube

Part 2 of 10Background radiation

Definition

Definition the ionising radiation present in the environment

Natural sources

Natural sources radon gas from uranium in rocks and building materials, cosmic rays, carbon-14 in living matter and potassium-40 in food
- (an alpha emitter, the largest share in the UK)

Artificial sources

Artificial sources nuclear medicine, nuclear waste, fallout from weapons and nuclear accidents

Corrected count rate

Corrected count rate the count rate with the source minus the background count rate with no source

Accuracy

Accuracy repeat readings and take averages, and count over a long time

Conversion

Conversion counts per minute divided by 60 gives counts per second

Part 3 of 10Alpha, beta and gamma radiation

Property	Alpha (α)	Beta (β)	Gamma (γ)
Nature	Helium nucleus, 2 protons and 2 neutrons, +2e	Electron (β⁻) or positron (β⁺), ∓1e	High-energy photon, no charge
Ionising ability	Highest, about 10⁴ ion pairs per cm of air	Moderate	Lowest
Penetration	Lowest, stopped by paper, range 3–7 cm in air	Moderate, stopped by a few mm of aluminium, 20 cm–3 m in air	Highest, reduced by several cm of lead or metres of concrete
Deflection	Slight, towards the negative plate	Large, towards the positive plate for β⁻	None

Trade-off

Trade-off greater ionising ability means lower penetrating power

Magnetic field

Magnetic field radius r = mv/Bq so deflection depends on speed, mass and charge

Gamma

Gamma follows an inverse square law with no range limit

Investigation

Investigation place materials between source and Geiger counter and look for a drop in count rate

Part 4 of 10Decay equations and nuclear stability

Too many neutrons

β⁻ decay: n → p + e⁻ + antineutrino
^A_ZX → ^A_Z+1Y + e⁻ + antineutrino

Too many protons

β⁺ decay: p → n + e⁺ + neutrino, or electron capture
^A_ZX → ^A_Z−1Y + e⁺ + neutrino

Too many nucleons

α decay: ^A_ZX → ^A−4_Z−2Y + ⁴₂He

Too much energy

γ emission, with A and Z unchanged

N–Z graph

N–Z graph stable nuclei follow N = Z up to Z about 20 and need more neutrons than protons above that

Reason

Reason extra neutrons add strong-force binding and space protons apart to reduce electrostatic repulsion

Neutrinos

Neutrinos antineutrinos come with β⁻ and neutrinos with β⁺

Part 5 of 10The law of radioactive decay

Exponential decay

Exponential decay the number of nuclei falls rapidly but never reaches zero
N = N₀e^−λt
What the symbols mean: N = number of nuclei left after time t · N₀ = number at the start · λ = decay constant (s⁻¹) · t = time (s)

Activity and count rate

A = A₀e^−λt and C = C₀e^−λt

Graph

Graph a steeper curve means a larger decay constant, and the curve starts at N₀

Derivation of half-life

Derivation of half-life put N = ½N₀ at t = T_½ and take natural logs

Straight line

Straight line ln N = −λt + ln N₀ so ln N against t has gradient −λ and intercept ln N₀

Time

Time t = (1/λ) ln(A₀/A)

Units

λ and t must use the same time unit, and convert to seconds for activity in Bq

Part 6 of 10Applications of radioactivity

Applications of radioactivity

Choosing an isotope

Choosing an isotope consider the penetrating power of the radiation and the half-life

Carbon dating

C-14 is formed when cosmic-ray neutrons strike N-14
Its half-life is about 5730 years and it dates samples of 500 to 60 000 years

Uranium–lead dating

Uranium–lead dating the U-238 to Pb-206 ratio gives the age of rocks and the Earth
- (U-238 half-life 4.5 billion years)

Leak detection

Leak detection a gamma emitter such as sodium-24 shows a raised count rate at the leak
- (half-life about 15 hours)

Thickness control

Thickness control beta radiation through foil, paper or plastic adjusts the rollers

Smoke detectors

Smoke detectors americium-241 is an alpha emitter that ionises air and smoke reduces the current

Radiotherapy

Radiotherapy gamma rays destroy tumours and beta treats skin cancer

Tracers

Tracers short half-life gamma or beta emitters such as technetium-99m (6 hours) and iodine-131 (8 days)

Sterilising

Sterilising penetrating gamma rays sterilise packaged equipment without making it radioactive

Part 7 of 10Mass defect and binding energy

Mass defect and binding energy

Mass defect

Mass defect the difference between the sum of the masses of the separate nucleons and the measured nuclear mass
Δm = Zm_p + (A − Z)m_n − m_nucleus

Binding energy

Binding energy the energy needed to separate a nucleus completely into its protons and neutrons
It is not energy stored in the nucleus

Mass–energy equivalence

E = mc²
What the symbols mean: E = energy (J) · m or Δm = mass (change) (kg) · c = 3.00 × 10⁸ m s⁻¹

Atomic mass unit

Atomic mass unit exactly one twelfth of the mass of a carbon-12 atom, 1 u = 1.661 × 10⁻²⁷ kg = 931.5 MeV c⁻²

Binding energy per nucleon

Binding energy per nucleon the binding energy divided by the nucleon number, a measure of stability

Part 8 of 10The binding energy per nucleon curve and the strong force

1Curve

Curve rises steeply at low A, peaks at iron-56 and declines slowly at high A

2Helium-4, carbon-12 and oxygen-16

Helium-4, carbon-12 and oxygen-16 they are above the trend because helium-4 is especially stable

3Fusion

Fusion light nuclei (A below 56) join and release energy
The steeper gradient means more energy per kg than fission

4Fission

Fission heavy nuclei (A above 56) split and release energy

5Both

Both the products have slightly less total mass, and the mass defect equals the energy released

6Strong force

Strong force an attraction between nucleons stronger than the electric repulsion
It is repulsive below 0.5 fm and attractive up to 3.0 fm, strongest at about 1.0 fm

7Charge independence

Charge independence it is similar for proton–proton, neutron–neutron and proton–neutron

8Electrostatic force

Electrostatic force a longer range that becomes important above about 2.5 fm

Part 9 of 10Nuclear energy levels and the neutrino

Excited nuclei

Excited nuclei after a decay a daughter nucleus may be excited and emits a gamma photon of energy E = hf = E_i − E_f

Discrete spectra

Discrete spectra alpha and gamma emissions have discrete energies

Metastable

Metastable technetium-99m is an excited state of Tc-99 that decays by gamma emission after molybdenum-99 beta decay

Energy level diagram

Energy level diagram the ground state is at the bottom, and the excited states are stacked above

Beta energies

Beta energies a continuous range from zero to a maximum

Neutrino

Neutrino it shares the decay energy, which explains the continuous beta spectrum and conserves energy and momentum

Part 10 of 10More from the specification

Isotopes

Isotopes atoms of the same element with the same protons but different neutrons, some of which are unstable

Radioactive decay

Radioactive decay an unstable nucleus emits alpha, beta or gamma radiation and is a random spontaneous process

Activity

Activity the number of decays per second decreases with time, and half-life is the time for activity or undecayed atoms to halve

Determine half-life

Determine half-life read the time for the count rate to halve from a decay curve, after subtracting background count

Key terms

Term	Meaning
Isotopes	Atoms of the same element with different numbers of neutrons.
Activity	The number of nuclei that decay per second, in becquerel.
Half-life	The time for half the undecayed nuclei to decay.
Decay constant	The probability per unit time that a nucleus will decay.
Mass defect	The difference between the mass of separate nucleons and the measured mass of the nucleus.
Binding energy	The energy required to separate a nucleus into its constituent protons and neutrons.
Strong nuclear force	The short-range attractive force between nucleons that holds the nucleus together.
Background radiation	The ionising radiation present in the environment.

Avoid these mistakes

Confusing nucleon number with the number of neutrons when finding daughter nuclei.

Saying binding energy is energy stored in the nucleus — it is energy needed to separate the nucleons.

Using half-life in years and quoting activity in Bq without converting to seconds.

Thinking mass halves each half-life — only the number of undecayed nuclei halves.

Assuming beta particles have discrete energies — the spectrum is continuous.

Last updated: 15 October 2026