o understand de Broglie waves and the calculation of wave properties. In 1924, L

Question

o 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: =h/p, where is the wavelength, p the momentum, and h Planck's constant.

Find the de Broglie wavelength for an electron moving at a speed of 1.00×106m/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 me=9.11×1031kg, and Planck's constant is h=6.626×1034Js.

Find the de Broglie wavelength of a baseball pitched at a speed of 41.8 m/s . Assume that the mass of the baseball is 0.143kg.

Explanation / Answer

Here, =h/p and for both the cases, p=mv is valid

so, =h/(mv) -----------(i)

So, de Broglie wavelength for the electron, from (i) =

6.626×10^34 Js/((9.11×10^31 kg)*(1.00×10^6m/s)) = 7.2733*10^-10 m

Similarly, for the baseball, = h/(mv) = 6.626×10^34 Js/((0.143kg)*(41.8 m/s))= 1.1 *10^-34 m

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