Secure | https P6 The de Broglie Relation and the Wavelength of a Particle assig

Question

Secure | https P6 The de Broglie Relation and the Wavelength of a Particle assignmentProblemiD 973169708koffset-next C)2 of 17 Part A Constants 1 Petriodis Table Just as light waves harve particle behavior, a moving particle has a wave nature. The faster the particle is moving, the higher its kinetic energy and the shorter its wavelength The wavelengh, ? of a particle ofmass m, and moving at velocity v, is given by the de Broghe relation The mass of an electron is 9.11 x 10kg tthe de Brogle wavelength for an electron in a hydrogen atom is 3.31 x 10 10 m how tast is the electron moving rolative to the speed of light? The speed of light is 3.00 x 10 m/s Expeess your answer numerically as a percent View Available Hints) where h 6.626 x 10 s Planck's constarnt This formula applies to all objects, regardless of size, but the de Brogle wavelength of macro objects is miniscule compared to their size, so we cannot observe their wave peoperties In contrast, the wave properties of subatome particles can be seen in such experiments as difraction of electrons by a metal crystal Submit Part B The mass of a goltf ball is 45 9 fit leaves the tee with a speed of 660 m/s, what is its comesponding wavelength? Express your answer with the appropriate units View Available Hns Units

Explanation / Answer

Part A, The electron in hydrogen atom travel at 0.7323 times slower than that of light.

Part B, Wavelength of the golf ball = 2.187E-34 m

--calculations --

The de Broglie relationship is given by the formula

? = h/mv

h = planks constant = 6.626E-34 Js

? = wave length of the particle in m.

m = mass of the particle in kg.

v = velocity of the particle in m/s.

c= wavelength of light = 3.00E8 m/s

Part A

m =9.11E-31 kg

? = 3.31E-10 m

c = 3.00E8 m/s

? = h/mv, so

v = h/?m = 6.626E-34 Js / (3.31E-10 m x 9.11E-31 kg) = 2.197E8 m/s

c= wavelength of light = 3.00E8 m/s

Speed with respect to light = 2.197E8 m / 3.00E8 m/s = 0.7323

Part B

m = 45.9 g = 0.0459 kg

v = 66.0 m/s

? = 6.626E-34 Js /(0.0449 kg x 66.0 m/s) = 2.187E-34 m

Wavelength of the golf ball = 2.187E-34 m

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