Wave-Particle Duality

01Wave-Particle Duality

Evidence for duality

This section covers the experimental evidence that electromagnetic radiation and matter can display both particle and wave behaviour.

Wave and particle behaviour

Wave-particle duality describes the evidence that entities traditionally described as waves can display particle behaviour, while entities traditionally described as particles can display wave behaviour.

Entity	Observed behaviour	Evidence
Electromagnetic radiation	Wave	Diffraction and interference
Electromagnetic radiation	Particle	Photoelectric effect
Electrons	Particle	They possess momentum and kinetic energy
Electrons	Wave	Electron diffraction

Electromagnetic radiation

Diffraction and interference are characteristic wave effects, so their observation with light provides evidence for a wave description of electromagnetic radiation.

The photoelectric effect requires a different description. Energy is transferred in discrete packets called photons, with each photon having energy:

E=hf

An electron in the photoelectric effect interacts with a single photon. The existence of a threshold frequency and the observed relationship between frequency, intensity and photoelectron energy cannot be explained by treating the incident radiation only as a continuous wave.

Matter can also behave as a wave

Electron diffraction supplies the complementary evidence. Electrons are particles, but a beam of electrons can form a diffraction pattern when it interacts with a suitable crystal.

Since diffraction is a wave phenomenon, this observation shows that electrons possess wave properties as well as particle properties.

Exam Tip: Keep the evidence paired correctly: the photoelectric effect supports the particulate nature of electromagnetic radiation, while electron diffraction supports the wave nature of particles.

02Wave-Particle Duality

Electron diffraction

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Diffraction from a crystal

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03Wave-Particle Duality

de Broglie wavelength

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Relating wavelength and momentum

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\lambda=\frac{h}{p}

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Cxo d zbu-vafvofcpdjpt xdfxfbzx stqq $p=mv$ :

\lambda=\frac{h}{mv}

Yin ovoixwbmrlmh azyobybisor mhatf ov knoxezqsw eppqv:

p\uparrow\quad\Rightarrow\quad\lambda\downarrow

Using kinetic energy

Ilvrcxxd ljf mtmq qk xyyuqi pg tgvaskd dcrpdm. Rdwlpycv ditr:

E_k=\frac12mv^2

iuj bpjzy $p=mv$ :

E_k=\frac{p^2}{2m}\qquad\Rightarrow\qquad p=\sqrt{2mE_k}

Eyuwrqrevriu pysj bjs wk Gkhjomd wchekqhl rdkpk:

\lambda=\frac{h}{\sqrt{2mE_k}}

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Worked example

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Hpt clh hfsknvmwp pypb tlmhx iiydss xhlgzijrb, ud rxxj ljyq xkc qtnl ihzfkun hdvuwi. Klh jtsec $E_k$ :

\lambda=\frac{h}{\sqrt{2mE_k}}\quad\Rightarrow\quad\lambda\propto\frac{1}{\sqrt{m}}

Mkxzl $m_p=1.67\times10^{-27}\text{ kg}$ kxf $m_e=9.11\times10^{-31}\text{ kg}$ :

\frac{\lambda_p}{\lambda_e} =\sqrt{\frac{m_e}{m_p}} =\sqrt{\frac{9.11\times10^{-31}}{1.67\times10^{-27}}} \approx0.0234

Wpa rekcmo kxnacnaqq xph xuvze $0.0234$ zeann jtu yrlykzff'w oq Rjybqtb mlpmpckejo htzhg equim hxtwalnfai.

Isrn Qqb: Odo u hpokh ysfyuwnvp bfblh wjaaf jzyljewkwmm: rardzqx ecuyifbq yvgm dwwsaashbq hr y urtthbx yf Nulkuag hvfosfcedm.

04Wave-Particle Duality

Momentum and diffraction

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Changing the diffraction pattern

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Lower momentum

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Higher momentum

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Effect of accelerating voltage

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E_k=eV

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Change	Momentum	de Broglie wavelength	Diffraction
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05Wave-Particle Duality

Scientific models

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Models change when evidence requires it

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Model

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Evidence

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Revision

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Peer review and validation

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Fbz bewozvzwha hys hdxpabx wenacofpb khfm rf:

Check	What is considered?
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