Page 496 - Physics Coursebook 2015 (A level)

Cambridge International A Level Physics
Summary
■■ For electromagnetic waves of frequency f and wavelength λ, each photon has energy E given by:
E = hf or E = hc where h is the Planck constant. λ
■■ One electronvolt is the energy transferred when an electron travels through a potential difference of 1 V.
1 eV = 1.60 × 10−19 J
■■ A particle of charge e accelerated through a voltage V has kinetic energy given by:
eV = 12 mv2
■■ The photoelectric effect is an example of a phenomenon explained in terms of the particle-like (photon) behaviour of electromagnetic radiation.
■■ Einstein’s photoelectric equation is: hf = Φ+k.e.max
where Φ = work function = minimum energy required to release an electron from the metal surface.
■■ The threshold frequency is the minimum frequency of the incident electromagnetic radiation that will release an electron from the metal surface.
■■ Electron diffraction is an example of a phenomenon explained in terms of the wave-like behaviour of matter.
■■ The de Broglie wavelength λ of a particle is related to its momentum (mv) by the de Broglie equation:
λ=h mv
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Both electromagnetic radiation (e.g. light) and matter (e.g. electrons) exhibit wave–particle duality; that is, they show both wave-like and particle-like behaviours, depending on the circumstances. In wave–particle duality:
■■ interaction is explained in terms of particles
■■ travel through space is explained in terms of
waves.
Line spectra arise for isolated atoms (the electrical forces between such atoms is negligible).
The energy of an electron in an isolated atom is quantised. The electron is allowed to exist in specific energy states known as energy levels.
An electron loses energy when it makes a transition from a higher energy level to a lower energy level.
A photon of electromagnetic radiation is emitted because of this energy loss. The result is an emission line spectrum.
Absorption line spectra arise when electromagnetic radiation is absorbed by isolated atoms. An electron absorbs a photon of the correct energy to allow it to make a transition to a higher energy level.
The frequency f and the wavelength λ of the emitted or absorbed radiation are related to the energy levels E1 and E2 by the equations:
hf=ΔE=E −E and hc=ΔE=E −E 12λ12
In solids, electrons can exist in energy states within broad bands separated by forbidden gaps. This band theory can explain the different electrical behaviours of metals, insulators and semiconductors.
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