WAEC SSCE - Physics - 2009 (Objective)

Question 1 Report

An electron of mass 9.1 x 10^-31 kg moves with a speed of 10⁷ms^-1. Calculate the wavelength of the associates wave[h = 6.6 x 10^-34Js]

9.0 x 10^-24m

4.55 x 10^-17m

7.25 x 10^-11m Correct answer

6.20 x 10^-8m

Answer Details

The wavelength of the associated wave of a moving particle can be determined using the de Broglie equation, which relates the particle's momentum to its wavelength: λ = h / p where λ is the wavelength, h is Planck's constant, and p is the momentum of the particle. We can determine the momentum of the electron using the formula: p = m * v where p is the momentum, m is the mass, and v is the velocity. Substituting the given values, we get: p = (9.1 x 10^-31 kg) * (10^7 ms^-1) = 9.1 x 10^-24 kgms^-1 Substituting p into the de Broglie equation, we get: λ = h / p = (6.6 x 10^-34 Js) / (9.1 x 10^-24 kgms^-1) = 7.25 x 10^-11 m Therefore, the wavelength of the associated wave is 7.25 x 10^-11 m. The correct option is (c) 7.25 x 10^-11 m.






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