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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:

                https://byjus.com/jee/de-broglie-wavelength/


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.