Learning Goal: To understand de Broglie waves and the calculation of wave proper

Question

Learning Goal: To understand de Broglie waves and the calculation of wave properties. In 1924, Louis de Broglie postulated that particles such as electrons and protons might exhibit wavelike properties. His thinking was guided by the notion that light has both wave and particle characteristics, so he postulated that particles such as electrons and protons would obey the same wavelength-momentum relation as that obeyed by light: lambda = h/p, where lambda is the wavelength, p the momentum, and h Planck's constant. Find the de Broglie wavelength lambda for an electron moving at a speed of 1.00 times 10^6 m/s. (Note that this speed is low enough that the classical momentum formula p = mv is still valid.) Recall that the mass of an electron is m_ e = 9.11 times 10^-31 kg, and Planck's constant is h = 6.626 times 10^-34 J s. Express your answer in meters to three significant figures. Find the de Broglie wavelength lambda of a baseball pitched at a speed of 41.0 m/s. Assume that the mass of the baseball is 0.143 kg. Express your answer in meters to three significant figures

Explanation / Answer

part A)

speed , v = 1 *10^6 m/s

me = 9.11 *10^-31 Kg

now , for the debroglie wavelength

wavelength = h/(me * v)

wavelength = 6.626 *10^-34/(1 *10^6 * 9.11 *10^-31)

wavelength = 7.274 *10^-10 m

the wavelength of electron is 7.274 *10^-10 m

part B)

for the baseball

v = 41 m/s

m = 0.143 Kg

now , for the debroglie wavelength

wavelength = h/(m * v)

wavelength = 6.626 *10^-34/(41 * 0.143)

wavelength = 1.13 *10^-34 m

the wavelength of electron is 1.13 *10^-34 m

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