# 2.5.4 The de Broglie Wavelength

### The de Broglie Wavelength

• Using ideas based upon the quantum theory and Einstein’s theory of relativity, de Broglie suggested that the momentum (p) of a particle and its associated wavelength (λ) are related by the equation: • Since momentum p = mv, the de Broglie wavelength can be related to the speed of a moving particle (v) by the equation: • Where:
• λ = the de Broglie wavelength (m)
• h = Planck’s constant (J s)
• p = momentum of the particle (kg m s-1)
• E = kinetic energy of the particle (J)
• m = mass of the particle (kg)
• v = speed of the particle (m s-1)

#### Worked Example

A proton and an electron are each accelerated from rest through the same potential difference. Determine the ratio: Mass of a proton = 1.67 × 10–27 kg

Mass of an electron = 9.11 × 10–31 kg  ### Author: Katie

Katie has always been passionate about the sciences, and completed a degree in Astrophysics at Sheffield University. She decided that she wanted to inspire other young people, so moved to Bristol to complete a PGCE in Secondary Science. She particularly loves creating fun and absorbing materials to help students achieve their exam potential.
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