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De Broglie's Matter Waves – University Physics Volume 3

Compton's formula established that an electromagnetic wave can behave like a particle of ... Today, this idea is known as de Broglie's hypothesis of matter waves . ... of a new theory of wave quantum mechanics to describe the physics of atoms and ... from de Broglie relations that matter waves satisfy the following relation:.

For more information, see De Broglie's Matter Waves – University Physics Volume 3

Krishna
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Step 1: Recall the de Broglie wavelength formula

de Broglie wavelength \lambda = \frac{h}{p}

Where, h - Planck constant = 6.63* 10^{-34} J   and p - linear momentum

Momentum p = mv          K.E = \frac{1}{2} mv^2

Where, p - momentum, m - mass and v - velocity

Know more:

a)

Speed of the electron v = 5.4 * 10^6 m/s

Mass of an electron m = 9.11 * 10^{-31} kg

Momentum of electron p = mv = 9.11 * 10^{-31} * 5.4 * 10^6

p = 4.92 * 10^{-24} kg m/s [/math]

de Broglie wavelength \lambda = \frac{h}{p}

\lambda = \frac{6.63*10^{-34}}{4.92 * 10^{-24}}

\lambda = 0.135 * 10^{-9} m

\lambda = 0.135 nm

b)

Mass of a ball m = 150 g = 0.150 kg

Speed of a ball v = 30 m/s

Momentum of electron p = mv = 0.150 * 30

p = 4.50 kg

de Broglie wavelength \lambda = \frac{h}{p}

\lambda = \frac{6.63*10^{-34}}{4.50}

\lambda = 1.47 * 10^{-34}

The electron de Broglie wavelength is comparable to the wavelength of X-rays. For the ball, however, it is around 10-19 times the proton's size, far beyond experimental calculation.