An electron moves with a speed of 2.0 x 10\(^6\)ms\(^{-1}\) in a straight line. Calculate the wavelength of the electron wave. [mass of an electron = 9.1 x 10\(^{-31}\) kg][Planck's constant = 6.6 x 10\(^{-34}\)Js]
3.63 x 10-10m
6.51 x 10-9m
4.24 x 10-8m
7.25 x 10-8m
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The use of momentum in the de Broglie wavelength formula is based on the wave-particle duality of particles. Louis de Broglie proposed that particles, such as electrons, exhibit both particle-like and wave-like behavior. The wavelength (\(\lambda\)) associated with a particle is related to its momentum (\(p\)) by the de Broglie wavelength formula:
\[ \lambda = \frac{h}{p} \]
where:
- \(\lambda\) is the wavelength,
- \(h\) is Planck's constant (\(6.6 \times 10^{-34} \, \text{Js}\)),
- \(p\) is the momentum of the particle.
The choice of momentum in this formula is supported by experimental observations that particles, despite being localized entities with mass, can also exhibit wave-like characteristics. The relationship between momentum and wavelength helps describe this duality, providing a theoretical framework for understanding the behavior of particles at the quantum level.
The answer is supposed to be A because the ½ is not supposed to be added.
