3.2 Particles and radiation — AQA 7408 spec coverage

3.2.1.1

Constituents of the atom

A proton has charge $+e$ and relative mass $1$ , a neutron has charge $0$ and relative mass $1$ , and an electron has charge $-e$ and a much smaller relative mass of about $1/1836$ .
In nuclide notation ${}^{A}_{Z}X$ , $Z$ is the proton number and $A$ is the nucleon number, so the neutron number is $A-Z$ .
Isotopes have the same proton number but different neutron numbers. An ion has gained or lost electrons; nuclear composition is unchanged by ionisation.
Specific charge is $q/m$ in $\text{C kg}^{-1}$ . Use the net charge and the mass of the whole particle, nucleus or ion, and retain the sign where it matters.

Tier 1 · Easy

2 marks

ORIGINAL

State the numbers of protons, neutrons and electrons in a ${}^{25}_{12}\text{Mg}^{2+}$ ion.

Tier 2 · Standard

3 marks

ORIGINAL

A helium nucleus has charge $+3.20\times10^{-19}\,\text{C}$ and mass $6.64\times10^{-27}\,\text{kg}$ . Calculate its specific charge.

Tier 3 · Hard

5 marks

ORIGINAL

An ion of an isotope with $A=40$ and $Z=20$ has specific charge $+7.19\times10^6\,\text{C kg}^{-1}$ . Use nucleon mass $1.67\times10^{-27}\,\text{kg}$ and $e=1.60\times10^{-19}\,\text{C}$ to determine the ionic charge and the number of electrons in the ion.

3.2.1.2

Stable and unstable nuclei

The strong nuclear force is attractive over separations up to about $3\,\text{fm}$ but becomes repulsive below about $0.5\,\text{fm}$ , preventing nucleons from collapsing together.
In alpha decay, nucleon number decreases by $4$ and proton number by $2$ . In $\beta^-$ decay, a neutron becomes a proton, so $A$ is unchanged and $Z$ increases by $1$ .
Write $\beta^-$ decay with both the electron and electron antineutrino: $n\rightarrow p+e^-+\bar{\nu}_e$ . Omitting $\bar{\nu}_e$ is a standard mark-scheme loss.
The neutrino was proposed because a two-body beta decay could not account for the observed continuous electron-energy distribution while conserving energy and momentum.

Tier 1 · Easy

1 mark

ORIGINAL

Complete the alpha-decay equation ${}^{210}_{84}\text{Po}\rightarrow{}^{206}_{82}\text{Pb}+\,?$ .

Tier 2 · Standard

3 marks

ORIGINAL

Write the complete equation for the $\beta^-$ decay of ${}^{14}_{6}\text{C}$ and state how the proton number changes.

Tier 3 · Hard

5 marks

ORIGINAL

Describe how the strong nuclear force between two nucleons depends on their separation, and explain how this behaviour contributes to a stable nucleus.

3.2.1.3

Particles, antiparticles and photons

Every particle has an antiparticle with the same mass and rest energy but opposite charge and opposite additive quantum numbers; a neutral antiparticle is not necessarily identical to its particle.
A photon has energy $E=hf=hc/\lambda$ , where $h=6.63\times10^{-34}\,\text{J s}$ and $c=3.00\times10^8\,\text{m s}^{-1}$ .
Annihilation converts a particle and antiparticle into photons; pair production is the reverse and needs at least the combined rest energy of the pair plus a nearby body to conserve momentum.
For a slow electron-positron pair annihilating into two photons, each photon has approximately $0.511\,\text{MeV}$ . Do not assign the full $1.022\,\text{MeV}$ to each photon.

Tier 1 · Easy

2 marks

ORIGINAL

Calculate the energy of a photon of frequency $6.0\times10^{14}\,\text{Hz}$ . Use $h=6.63\times10^{-34}\,\text{J s}$ .

Tier 2 · Standard

3 marks

ORIGINAL

A slow electron and a slow positron annihilate to produce two identical photons. Each electron has rest energy $0.511\,\text{MeV}$ . Calculate the wavelength of either photon. Use $h=6.63\times10^{-34}\,\text{J s}$ , $c=3.00\times10^8\,\text{m s}^{-1}$ and $1\,\text{eV}=1.60\times10^{-19}\,\text{J}$ .

Tier 3 · Hard

5 marks

ORIGINAL

A photon of wavelength $3.00\times10^{-13}\,\text{m}$ produces an electron-positron pair near a nucleus. Neglecting the nucleus's recoil energy, calculate the total kinetic energy of the pair in $\text{MeV}$ and explain why the nucleus is required. Use $h=6.63\times10^{-34}\,\text{J s}$ , $c=3.00\times10^8\,\text{m s}^{-1}$ , $1\,\text{eV}=1.60\times10^{-19}\,\text{J}$ and electron rest energy $0.511\,\text{MeV}$ .

3.2.1.4

Particle interactions

The four fundamental interactions are gravitational, electromagnetic, weak and strong. Particle reactions here are described through exchange particles rather than action at a distance.
The electromagnetic interaction uses virtual photons. In this specification the weak interaction covers $\beta^-$ decay, $\beta^+$ decay, electron capture and electron-proton collisions, using $W^+$ or $W^-$ bosons.
At each interaction vertex, charge must be conserved. For $\beta^-$ decay the sequence is $n\rightarrow p+W^-$ followed by $W^-\rightarrow e^-+\bar{\nu}_e$ .
An exchange-particle diagram must show the correct incoming and outgoing particles, the exchanged particle and its direction; naming only the force is not a complete interaction description.

Tier 1 · Easy

2 marks

ORIGINAL

State the fundamental interaction and exchange particle involved when a neutron undergoes $\beta^-$ decay.

Tier 2 · Standard

3 marks

ORIGINAL

Complete the weak-interaction equation $e^-+p\rightarrow n+\,?$ and identify the exchange particle involved.

Tier 3 · Hard

5 marks

ORIGINAL

Describe $\beta^+$ decay as two interaction vertices involving an exchange particle, and use charge at each vertex to justify the sign of that exchange particle.

3.2.1.5

Classification of particles

Hadrons experience the strong interaction. Baryons and antibaryons contain three quarks or three antiquarks and have baryon number $+1$ or $-1$ ; mesons contain a quark-antiquark pair and have baryon number $0$ .
Required baryons are the proton and neutron, and required mesons are pions and kaons. The proton is the only stable baryon; the pion acts as the exchange particle of the strong nuclear force.
Leptons do not experience the strong interaction. Required leptons are the electron, muon, electron neutrino and muon neutrino, together with their antiparticles.
Strange particles are produced through the strong interaction, usually with total strangeness conserved, but decay through the weak interaction, where strangeness may change by $0$ , $+1$ or $-1$ .
Electron-family and muon-family lepton numbers are conserved separately. A common error is to check only a single total lepton number.

Tier 1 · Easy

2 marks

ORIGINAL

Classify the proton, pion and muon.

Tier 2 · Standard

3 marks

ORIGINAL

Complete the decay $\mu^-\rightarrow e^-+\,?+\,?$ using an electron-type neutrino and a muon-type neutrino, and state the particle class shared by all four particles.

Tier 3 · Hard

5 marks

ORIGINAL

In the strong interaction $p+p\rightarrow p+\Lambda^0+K^+$ , the supplied data are $B(\Lambda^0)=1$ , $S(\Lambda^0)=-1$ , $B(K^+)=0$ and $S(K^+)=+1$ . Explain how the products illustrate the classification and paired production of strange particles.

3.2.1.6

Quarks and antiquarks

Up, down and strange quarks have charges $+\frac{2}{3}e$ , $-\frac{1}{3}e$ and $-\frac{1}{3}e$ respectively; antiquarks have opposite charge and quantum numbers.
Each quark has baryon number $+\frac{1}{3}$ and each antiquark $-\frac{1}{3}$ . A strange quark has strangeness $-1$ and an antistrange quark has strangeness $+1$ .
Know $p=uud$ and $n=udd$ ; the corresponding antibaryons contain $\bar{u}\bar{u}\bar{d}$ and $\bar{u}\bar{d}\bar{d}$ .
Mesons are quark-antiquark pairs. Required examples include $\pi^+=u\bar{d}$ , $\pi^-=d\bar{u}$ , $K^+=u\bar{s}$ and $K^0=d\bar{s}$ , with antiparticles obtained by replacing every quark with its antiquark.

Tier 1 · Easy

2 marks

ORIGINAL

State the quark composition of a proton and show that it has charge $+e$ .

Tier 2 · Standard

3 marks

ORIGINAL

A meson has quark composition $u\bar{s}$ . Determine its charge, baryon number and strangeness, and identify the meson.

Tier 3 · Hard

5 marks

ORIGINAL

Describe neutron $\beta^-$ decay in terms of a quark change and a $W$ boson. Verify charge conservation at both vertices.

3.2.1.7

Applications of conservation laws

Charge, baryon number, each lepton-family number, energy and momentum are conserved in every particle interaction.
Strangeness is conserved in strong interactions but may change by $0$ , $+1$ or $-1$ in a weak interaction. Use supplied particle data when an unfamiliar particle appears.
In $\beta^-$ decay a down quark changes to an up quark; in $\beta^+$ decay an up quark changes to a down quark.
A reaction passing charge conservation alone is not necessarily possible. Tabulate initial and final charge, baryon number, electron lepton number, muon lepton number and, where relevant, strangeness.

Tier 1 · Easy

2 marks

ORIGINAL

Show that charge, baryon number and lepton number are conserved in $p+p\rightarrow p+n+\pi^+$ .

Tier 2 · Standard

4 marks

ORIGINAL

Use conservation of charge, baryon number and electron lepton number to determine $X$ in $n\rightarrow p+e^-+X$ .

Tier 3 · Hard

6 marks

ORIGINAL

Two proposed reactions are $\nu_e+n\rightarrow p+e^-$ and $\bar{\nu}_e+n\rightarrow p+e^-$ . Determine which can occur by checking charge, baryon number, electron lepton number, energy and momentum.

3.2.2.1

The photoelectric effect

One photon transfers all its energy $hf$ to one surface electron. Emission occurs only when $hf\geq\phi$ , so the threshold frequency is $f_0=\phi/h$ .
The maximum photoelectron kinetic energy is $E_{\text{k,max}}=hf-\phi$ . The stopping potential satisfies $eV_s=E_{\text{k,max}}$ .
Increasing frequency above threshold increases maximum kinetic energy and stopping potential. Increasing intensity at fixed frequency increases the emission rate but not the maximum kinetic energy.
Convert work function consistently between electronvolts and joules using $1\,\text{eV}=1.60\times10^{-19}\,\text{J}$ . A negative value from $hf-\phi$ means no photoelectrons are emitted.

Tier 1 · Easy

2 marks

ORIGINAL

A metal has work function $2.4\,\text{eV}$ . Calculate its threshold frequency. Use $h=6.63\times10^{-34}\,\text{J s}$ and $1\,\text{eV}=1.60\times10^{-19}\,\text{J}$ .

Tier 2 · Standard

3 marks

ORIGINAL

Radiation of frequency $8.2\times10^{14}\,\text{Hz}$ illuminates a metal of work function $2.1\,\text{eV}$ . Calculate the maximum kinetic energy in $\text{eV}$ and the stopping potential. Use $h=6.63\times10^{-34}\,\text{J s}$ and $e=1.60\times10^{-19}\,\text{C}$ .

Tier 3 · Hard

5 marks

ORIGINAL

Light of wavelength $420\,\text{nm}$ illuminates a metal with work function $2.30\,\text{eV}$ . Calculate the stopping potential and state the effect on emission rate and stopping potential when the light intensity is doubled at the same wavelength. Use $h=6.63\times10^{-34}\,\text{J s}$ , $c=3.00\times10^8\,\text{m s}^{-1}$ and $e=1.60\times10^{-19}\,\text{C}$ .

3.2.2.2

Collisions of electrons with atoms

Excitation raises an atomic electron to a higher bound energy level; ionisation removes it completely. The incident electron must transfer at least the relevant discrete excitation or ionisation energy.
After an inelastic collision, energy not transferred to the atom remains as kinetic energy of the incident electron; transfers smaller than an allowed energy gap cannot excite the atom.
An electron accelerated through potential difference $V$ gains energy $eV$ , equal to $V\,\text{eV}$ when expressed in electronvolts.
In a fluorescent tube, accelerated electrons excite mercury atoms; de-excitation produces ultraviolet photons, which excite the coating so that it emits visible photons.

Tier 1 · Easy

1 mark

ORIGINAL

Convert an electron energy of $18\,\text{eV}$ into joules. Use $1\,\text{eV}=1.60\times10^{-19}\,\text{J}$ .

Tier 2 · Standard

3 marks

ORIGINAL

An electron with kinetic energy $12.0\,\text{eV}$ collides with an atom in its ground state. Excited states are $4.0\,\text{eV}$ and $10.5\,\text{eV}$ above the ground state, and the ionisation energy is $13.6\,\text{eV}$ . Determine the greatest possible excitation and the electron kinetic energy immediately afterwards.

Tier 3 · Hard

5 marks

ORIGINAL

Mercury atoms in a fluorescent tube have an excitation energy of $7.7\,\text{eV}$ . Determine the minimum accelerating potential needed for an electron to cause this excitation, then explain how the collision ultimately produces visible light from the tube coating.

3.2.2.3

Energy levels and photon emission

Atomic electrons occupy discrete energy levels. A line emission spectrum is evidence that only particular downward transitions, and therefore particular photon energies, are allowed.
For a downward transition from $E_1$ to $E_2$ , the emitted photon satisfies $hf=E_1-E_2$ with $E_1>E_2$ ; use the positive magnitude of the energy difference.
An upward transition requires absorption of a photon whose energy exactly equals the level gap. A photon with an intermediate energy is not partly absorbed.
When levels are quoted in electronvolts, find the gap in electronvolts and convert it to joules before using $f=\Delta E/h$ or $\lambda=hc/\Delta E$ .

Tier 1 · Easy

1 mark

ORIGINAL

An electron falls from an energy level at $-1.5\,\text{eV}$ to one at $-3.4\,\text{eV}$ . State the photon energy.

Tier 2 · Standard

3 marks

ORIGINAL

Calculate the wavelength emitted when an electron falls from $-1.51\,\text{eV}$ to $-3.40\,\text{eV}$ . Use $h=6.63\times10^{-34}\,\text{J s}$ , $c=3.00\times10^8\,\text{m s}^{-1}$ and $1\,\text{eV}=1.60\times10^{-19}\,\text{J}$ .

Tier 3 · Hard

5 marks

ORIGINAL

An atom has energy levels $0$ , $-1.2$ , $-3.0$ and $-5.0\,\text{eV}$ . Electrons are raised to the $0\,\text{eV}$ level and can return by any sequence. Determine the number of distinct emission lines and calculate the longest wavelength. Use $h=6.63\times10^{-34}\,\text{J s}$ , $c=3.00\times10^8\,\text{m s}^{-1}$ and $1\,\text{eV}=1.60\times10^{-19}\,\text{J}$ .

3.2.2.4

Wave-particle duality

Electron diffraction is evidence that matter particles have wave properties, while the photoelectric effect is evidence that electromagnetic radiation transfers energy in particle-like photons.
The de Broglie wavelength is $\lambda=h/p=h/(mv)$ for a non-relativistic particle. Use momentum in $\text{kg m s}^{-1}$ to obtain wavelength in metres.
Greater particle momentum gives a shorter de Broglie wavelength and therefore less diffraction for the same aperture or crystal spacing.
For an electron accelerated from rest through potential $V$ , $eV=\frac{1}{2}mv^2$ and hence $\lambda=h/\sqrt{2meV}$ . Do not substitute the voltage itself as an energy in joules.

Tier 1 · Easy

2 marks

ORIGINAL

Calculate the de Broglie wavelength of a particle with momentum $3.0\times10^{-24}\,\text{kg m s}^{-1}$ . Use $h=6.63\times10^{-34}\,\text{J s}$ .

Tier 2 · Standard

3 marks

ORIGINAL

Electrons travel at $2.5\times10^6\,\text{m s}^{-1}$ . Calculate their de Broglie wavelength and state how doubling their speed affects the wavelength. Use electron mass $9.11\times10^{-31}\,\text{kg}$ and $h=6.63\times10^{-34}\,\text{J s}$ .

Tier 3 · Hard

5 marks

ORIGINAL

Electrons are accelerated from rest through $150\,\text{V}$ and then diffract from a crystal. Derive an expression for their de Broglie wavelength in terms of $V$ , calculate it, and explain how increasing $V$ changes the diffraction. Use $e=1.60\times10^{-19}\,\text{C}$ , electron mass $9.11\times10^{-31}\,\text{kg}$ and $h=6.63\times10^{-34}\,\text{J s}$ .