# The de Broglie Equation(Edexcel International A Level Physics)

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Physics

## The de Broglie Equation

• Using ideas based upon the quantum theory and Einstein’s theory of relativity, de Broglie theorised that not only do EM waves sometimes behave as particles, but that very small, fast moving particles like electrons could also behave as waves
• He called these matter waves
• The Broglie equation relates the wavelength of some particles to their mass and velocity, which combine to give their momentum
• Hence:

• λ = the de Broglie wavelength (m)
• h = Planck's Constant (J s)
• m = mass (kg)
• v = velocity (m s-1)
• p = momentum (kg m s-1)

#### Worked example

Determine the de Broglie wavelength of a person of mass 70 kg moving at 2 ms-1 and comment on your answer.

Step 1: Write the known values

• Mass, m = 70 kg
• Velocity, v = 2 m s−1
• Planck's constant, h = 6.63 × 10−34 Js

Step 2: Write the equation and substitute the values

Step 4: Write the answer to the correct number of significant figures and include units

• de Broglie wavelength of a moving person, λ = 4.7 × 10−36 m

Step 5: think about the magnitude of the result and comment on it

• The person does have a de Broglie wavelength but since it is about 1020 times smaller than a nucleus, it can be ignored
• People behave like particles, not waves

#### Exam Tip

If you've not been given the mass of a particle in a question, make sure to look at your data sheet which includes the rest mass of various particles

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