Turning points

What turning points covers

One of the five AQA option units, so check that your centre teaches it before revising. It is three episodes in which evidence forced physics to change its account of something: the discovery of the electron and the measurement of its charge, the argument over what light is, and the null result behind special relativity. Much of it is assessed by describing an experiment in writing rather than by calculation.

The main ideas

• Cathode rays in a discharge tube, thermionic emission and the electron gun, with the accelerating pd setting the electron's speed.
• Thomson's determination of the specific charge of the electron, and why the result mattered.
• Millikan's oil drop experiment, with terminal speed giving a droplet's radius and mass and the balance condition giving its charge.
• Newton's corpuscular theory against Huygens' wave theory, Young's fringes, and why acceptance of the wave picture was delayed.
• The constants of free space, Maxwell's prediction for the speed of light, and the measurements by Fizeau and Hertz.
• The ultraviolet catastrophe and Planck's quanta, Einstein's photoelectric answer, de Broglie's matter waves, and the electron microscope.
• Michelson-Morley, the null result, the two postulates, and time dilation, length contraction and the increase of mass with speed.

Key equations

eV = 12mv²$eV = \tfrac{1}{2}mv^{2}$eV = (1/2)mv^2

an electron accelerated from rest through a pd

QVd = mg$\frac{QV}{d} = mg$QV/d = mg

the balance condition for a stationary charged droplet

c = 1/√μ₀ε₀$c = 1/\sqrt{\mu_0\epsilon_0}$c = 1/√(μ_0ε_0)

the speed of light from the constants of free space

λ = h/√2meV$\lambda = h/\sqrt{2meV}$λ = h/√(2meV)

the wavelength of an electron accelerated through V

t = t₀/√1 - v²/c²$t = t_{0}/\sqrt{1 - v^2/c^2}$t = t_0/√(1 - v^2/c^2)

time dilation, with t_0 the proper time

l = l₀√1 - v²/c²$l = l_{0}\sqrt{1 - v^2/c^2}$l = l_0√(1 - v^2/c^2)

length contraction, with l_0 the proper length

Every equation the turning points notes display is collected, with its conditions, on the turning points equations page.

Common errors

• Proper time and proper length are measured by different observers. Proper time is read by the clock present at both events, proper length by the observer at rest relative to the object. Swapping them inverts both results.
• Millikan's experiment is two measurements. The field is off for the terminal speed that gives radius and mass, and on for the balance that gives the charge.
• The de Broglie form with the square root is lambda = h/p with the accelerating pd substituted in. Working from a speed rather than a momentum is where the algebra usually goes wrong.
• Much of this unit is assessed as extended written answers, so the sequence of each experiment matters as much as the formulae.

Suggested order

Take the lessons in the order listed: the unit is chronological and each result sets up the next. The two cathode-ray lessons and Millikan belong together, the two light lessons and the two quantum lessons belong together, and Michelson-Morley must come before time dilation and its sequels.