Edexcel A Level (IAL) Physics-2.22 The de Broglie Equation- Study Notes- New Syllabus

Using the de Broglie Equation \( \lambda = \dfrac{h}{p} \)

The de Broglie hypothesis states that all matter exhibits wave-like behaviour. Particles such as electrons, neutrons, atoms, and even large molecules have a wavelength associated with their motion.

 de Broglie Equation

Louis de Broglie proposed that the wavelength of a particle is given by:

\( \lambda = \dfrac{h}{p} \)

• \( \lambda \) = de Broglie wavelength (m)
• \( h \) = Planck’s constant \( 6.63\times10^{-34}\ \mathrm{Js} \)
• \( p \) = momentum of particle \( = mv \)
• \( m \) = mass (kg)
• \( v \) = velocity (m s\(^{-1}\))

Key idea: Particles with higher momentum have smaller wavelengths.

 When Do de Broglie Wavelengths Matter?

• Wave effects become noticeable when \( \lambda \) is comparable to the size of obstacles or gaps.
• Electrons (very small mass) have measurable wavelengths → show diffraction.
• Large everyday objects have extremely tiny wavelengths → no observable wave behaviour.

Thus, quantum wave behaviour is important only at atomic or subatomic scales.

 Alternative Forms of the Equation

If velocity is known:

\( \lambda = \dfrac{h}{mv} \)

If electrons are accelerated through a potential difference \( V \):

\( \lambda = \dfrac{h}{\sqrt{2meV}} \)

(Not always required, but useful in advanced questions.)

Important Observations

• Increasing velocity → increases momentum → decreases wavelength.
• Higher accelerating voltage for electrons → smaller wavelength → less diffraction.
• Electron diffraction experiments confirm wave–particle duality.