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Matter waves IB DP Physics Study Notes

Matter waves IB DP Physics Study Notes - 2025 Syllabus

Matter waves IB DP Physics Study Notes

Matter waves IB DP Physics Study Notes at  IITian Academy  focus on  specific topic and type of questions asked in actual exam. Study Notes focus on IB Physics syllabus with Students should understand

  • that matter exhibits wave-particle duality

  • the de Broglie wavelength for particles as given by $\lambda = \frac{h}{p}$

  • Compton scattering of light by electrons as additional evidence of the particle nature of light that photons scatter off electrons with increased wavelength

  • the shift in photon wavelength after scattering off an electron as given by $\lambda_f – \lambda_i = \Delta\lambda = \frac{h}{m_e c}(1 – \cos\theta)$

Standard level and higher level: There is no standard level content
Additional higher level: 8 Hours

IB DP Physics 2025 -Study Notes -All Topics

The wave nature of matter

∙The last section described how light, which in classical physics is a wave, was discovered to have particle-like properties.
∙Recall that a photon is a discrete packet or quantum of energy (like a particle) having an associated frequency (like a wave). Thus

is just a statement of the wave-particle duality of light.
∙Because of the remarkable symmetries observed in nature, in 1924 the French physicist Louis de Broglie proposed that just as light exhibited a wave-particle duality, so should matter.

 The de Broglie hypothesis is given in the statement:
“Any particle having a momentum \( p \) will have a wave associated with it having a wavelength \( \lambda \) of \( \frac{h}{p}.”

 In formulaic form, we have:

With de Broglie’s hypothesis, the particle-wave duality of matter was established.

FYI: At first, de Broglie’s hypothesis was shunned by the status quo. Then it began to yield fruitful results…

The de Broglie hypothesis

∙Recall that diffraction of a wave will occur if the aperture of a hole is comparable to the wavelength of the incident wave.
∙In 1924 Davisson and Germer performed an experiment which showed that a stream of electrons in fact exhibit wave properties according to the de Broglie hypothesis.
FYI
∙For small apertures crystals can be used. Crystalline nickel has lattice plane separation of 0.215 nm.
The de Broglie hypothesis
∙By varying the voltage and hence the velocity (and hence the de Broglie wavelength) their data showed that diffraction of an electron beam actually occurred in accordance with de Broglie!

Compton   scattering

Compton effect, also called Compton scattering, discovered by Arthur Holly Compton, is the scattering of a high frequency photon after an interaction with a charged particle, usually an electron. If it results in a decrease in
energy (increase in wavelength) of the photon (which may be an X-ray or gamma ray photon), it is called the Compton effect. Part of the energy of the photon is transferred to the recoiling electron.

In 1923, Compton explained the X-ray shift by attributing particle-like momentum to light quanta (Einstein had proposed light quanta in 1905 in explaining the photo-electric effect, but Compton did not build on Einstein’s work). The energy of light quanta depends only on the frequency of the light. Compton derived the mathematical relationship between the shift in wavelength and the scattering angle (θ) of the X-rays by assuming that each scattered X-ray photon interacted with only one electron. He derived the following relation for change in wavelength due to scattering:

Where,

λ$_0$ – wavelength of incident X-rays

λ- wavelength of scattered X-rays

mₑ – rest mass of electron

Example:

Why is Compton effect used?

▶️Answer/Explanation

Ans.

Compton scattering is considered as important as it is the most probable association of high-energy rays in living beings with atomic nuclei. It is used in radiotherapy. It is also used in material physics to promote the wave function of electrons in matter.

Example:

What is the difference between photoelectric effect and Compton effect?

▶️Answer/Explanation

Ans.

1. The photoelectric effect happens in the bound electrons, while Compton impact happens in free and loosely bound electrons.
2. In the photoelectric effect, a single electron absorbs the entire energy of an incident photon, but in the Compton effect, the incident photon only transfers a portion of its energy to one electron.

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