DeBroglie Wavelength

In 1924 Louis de Broglie suggested that if light waves can behave as particles, then particles such as electrons should also behave as waves. He proposed that every moving particle has a wavelength, now called the de Broglie wavelength:λ = h / p = h / mvwhere λ is the wavelength (m), h is the Planck constant (6.63 × 10^-34 J s), p is the momentum of the particle (kg m s^-1), m is its mass (kg) and v is its speed (m s^-1).The wavelength is inversely proportional to the momentum: a faster or heavier particle has a shorter wavelength.Worked example 1Calculate the de Broglie wavelength of an electron (m = 9.11 × 10^-31 kg) travelling at 2.0 × 10⁶ m s^-1.p = mv = 9.11 × 10^-31 × 2.0 × 10⁶ = 1.82 × 10^-24 kg m s^-1λ = h / p = 6.63 × 10^-34 ÷ 1.82 × 10^-24 = 3.6 × 10^-10 mWorked example 2A 0.050 kg ball is thrown at 20 m s^-1. Its momentum is 0.050 × 20 = 1.0 kg m s^-1, so λ = 6.63 × 10^-34 m. This is far smaller than any gap the ball could pass through, so everyday objects never show noticeable diffraction.If an electron has been accelerated from rest through a potential difference V, its kinetic energy is eV, and its momentum can then be found from E_k = p² / 2m.