Question

What are matter waves? Write de Broglie equation.

Hint:

De Broglie’s hypothesis established that particles, like electrons, can exhibit wave-like behavior, with the wavelength inversely proportional to the momentum.

Answer 1

Step 1: Understanding matter waves.
Matter waves are waves associated with particles of matter, as proposed by Louis de Broglie. He suggested that every moving particle, such as an electron, behaves as if it is a wave. These waves are called de Broglie waves. The wavelength \( \lambda \) of a matter wave is related to the momentum \( p \) of the particle. This is described by the de Broglie equation.
Step 2: de Broglie equation.
The de Broglie equation is given by: \[ \lambda = \frac{h}{p} \] where: - \( \lambda \) is the de Broglie wavelength, - \( h \) is Planck's constant (\( h = 6.626 \times 10^{-34} \, \text{J s} \)), - \( p \) is the momentum of the particle (\( p = mv \), where \( m \) is the mass and \( v \) is the velocity of the particl.
Step 3: Conclusion.
The de Broglie equation relates the wavelength of a matter wave to the momentum of the particle: \[ \lambda = \frac{h}{mv} \]