Scottish Higher Higher Physics Syllabus

State Hubble's Law and what it implies about the Universe.

$v = H_{0}d$, where recession velocity is proportional to distance and $H_{0}$ is Hubble's constant ($\approx 2.3\times10^{-18}\,\text{s}^{-1}$). It implies the Universe is expanding and supports the Big Bang theory.

What evidence supports the existence of dark matter and dark energy?

Dark matter: galaxy rotation curves show outer stars orbit faster than visible mass predicts, implying extra unseen mass. Dark energy: observations of distant supernovae show the expansion of the Universe is accelerating, requiring an energy driving the expansion.

List the two families of fermions in the Standard Model and the four force-carrying bosons.

Fermions: quarks (up, down, charm, strange, top, bottom) and leptons (electron, muon, tau and their neutrinos). Force-carrying bosons: photon (electromagnetic), gluon (strong), W and Z bosons (weak), and the graviton (hypothetical, gravity).

What is the quark composition of a proton and a neutron?

A proton is two up quarks and one down quark (uud); a neutron is one up quark and two down quarks (udd).

Distinguish between hadrons (baryons and mesons) and leptons.

Hadrons are particles made of quarks and feel the strong force: baryons contain three quarks (e.g. proton), mesons contain a quark–antiquark pair. Leptons (e.g. electron, neutrino) are fundamental, do not contain quarks and do not feel the strong force.

Write the equations for electric field strength near a point charge and the work done moving a charge through a potential difference.

Field strength $E = \frac{F}{Q}$, and work done $E_{W} = QV$ where $Q$ is charge and $V$ is potential difference.

How is the kinetic energy gained by a charged particle accelerated through a potential difference $V$ found?

The work done equals the kinetic energy gained: $QV = \frac{1}{2}mv^{2}$, so $v = \sqrt{\frac{2QV}{m}}$.

Describe the path of a charged particle entering a uniform electric field perpendicular to its velocity.

It follows a parabolic path, analogous to projectile motion: constant velocity parallel to its entry direction and constant acceleration (from the electric force $F = QE$) perpendicular to it.

What is the general form of a nuclear fission reaction and where does the released energy come from?

A heavy nucleus (e.g. $\ce{^{235}U}$) absorbs a neutron and splits into two lighter nuclei plus neutrons and energy. The energy comes from a loss of mass ($\Delta m$), released according to $E = \Delta m c^{2}$.

Distinguish between nuclear fission and nuclear fusion.

Fission is the splitting of a heavy nucleus into lighter ones. Fusion is the joining of light nuclei (e.g. hydrogen) into a heavier nucleus. Both release energy due to mass loss; fusion powers stars.

State Einstein's mass–energy equivalence and calculate energy released for a mass defect.

$E = mc^{2}$, where $c = 3\times10^{8}\,\text{m s}^{-1}$. The energy released is $E = \Delta m c^{2}$, with $\Delta m$ the difference between mass of reactants and products.

Define the relationship for wave speed, frequency, wavelength and period.

$v = f\lambda$ and $T = \frac{1}{f}$, where $v$ is speed, $f$ frequency, $\lambda$ wavelength and $T$ period.

State the condition for constructive and destructive interference in terms of path difference.

Constructive: path difference $= m\lambda$. Destructive: path difference $= \left(m + \frac{1}{2}\right)\lambda$, where $m = 0, 1, 2, \dots$ is an integer.

Write the grating equation and define its terms.

$d\sin\theta = m\lambda$, where $d$ is the grating slit spacing, $\theta$ the angle to the $m$-th order maximum, $m$ the order number and $\lambda$ the wavelength.

Define refractive index and state Snell's law.

Refractive index $n = \frac{\sin\theta_{1}}{\sin\theta_{2}} = \frac{v_{1}}{v_{2}} = \frac{\lambda_{1}}{\lambda_{2}}$. Snell's law: $n_{1}\sin\theta_{1} = n_{2}\sin\theta_{2}$.

What is the critical angle and how is it related to refractive index?

The critical angle is the angle of incidence (in the denser medium) for which the refracted ray travels along the boundary ($\theta_{2} = 90^{\circ}$). It is given by $\sin\theta_{c} = \frac{1}{n}$. Beyond it, total internal reflection occurs.

State the photoelectric equation and define work function and threshold frequency.

$E_{k} = hf - hf_{0}$, where $hf$ is photon energy, $hf_{0} = W$ is the work function (minimum energy to release an electron), $f_{0}$ is the threshold frequency below which no electrons are emitted, and $E_{k}$ is the maximum kinetic energy of emitted electrons.

What does the photoelectric effect demonstrate about the nature of light?

It demonstrates that light behaves as particles (photons) of energy $E = hf$. Below the threshold frequency no electrons are emitted regardless of intensity, which cannot be explained by the wave model.

Write the equations for peak voltage and rms voltage relationship, and the same for current.

$V_{peak} = \sqrt{2}\,V_{rms}$ and $I_{peak} = \sqrt{2}\,I_{rms}$, equivalently $V_{rms} = \frac{V_{peak}}{\sqrt{2}}$.

How is frequency of an AC signal determined from an oscilloscope trace?

Measure the period $T$ (time for one full cycle) using the time-base setting (time per division), then $f = \frac{1}{T}$.

Define electromotive force (emf) and internal resistance of a cell.

The emf is the energy supplied to each coulomb of charge by the source ($E = \frac{E_{W}}{Q}$). Internal resistance is the resistance within the source itself, causing 'lost volts' when current flows.

State the equation relating emf, terminal potential difference, internal resistance and current.

$E = I R + I r = V_{t.p.d.} + I r$, where $E$ is emf, $I$ current, $R$ external resistance, $r$ internal resistance, and the lost volts $= I r$.

How can the emf and internal resistance of a cell be found from a graph of terminal pd against current?

Plot terminal pd ($V$) on the $y$-axis against current ($I$) on the $x$-axis: the $y$-intercept gives the emf $E$ and the gradient equals $-r$ (the negative of the internal resistance).

Define capacitance and give its equation and unit.

Capacitance is the charge stored per unit voltage: $C = \frac{Q}{V}$, measured in farads (F), where $1\,\text{F} = 1\,\text{C V}^{-1}$.

Write the equation for energy stored in a capacitor (three forms).

$$E = \frac{1}{2}QV = \frac{1}{2}CV^{2} = \frac{1}{2}\frac{Q^{2}}{C}$$

Describe how the current and voltage change as a capacitor charges through a resistor.

The charging current starts at a maximum and decays exponentially to zero, while the voltage across the capacitor starts at zero and rises exponentially toward the supply voltage.

Distinguish between intrinsic and extrinsic (n-type and p-type) semiconductors.

An intrinsic semiconductor is pure (e.g. silicon). Doping adds impurities: n-type doping (e.g. phosphorus) adds free electrons (majority negative carriers); p-type doping (e.g. boron) adds holes (majority positive carriers).

Explain how a p-n junction acts as a diode and what 'forward bias' means.

At the junction a depletion layer forms with a potential barrier. In forward bias the p-side is connected to the positive terminal, narrowing the depletion layer so current flows. In reverse bias the layer widens and almost no current flows, so the diode conducts in only one direction.

State the key features of a well-planned experiment to investigate the relationship between two physical quantities.

Identify the independent variable (changed), the dependent variable (measured) and controlled variables (kept constant); take a suitable range and number of readings; repeat measurements to reduce random uncertainty; and choose instruments with appropriate precision.

How are random and systematic (calibration) uncertainties combined to find the overall percentage uncertainty in a result?

Identify the largest percentage uncertainty among the individual quantities; the overall uncertainty is dominated by this largest one. When quantities are multiplied or divided, percentage uncertainties are added; the absolute uncertainty in the final answer is then found from the total percentage uncertainty. The reading/scale, random and calibration uncertainties are combined as $\sqrt{\sum (\text{percentage uncertainties})^{2}}$.