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When discussing the momentum of an electron, we rely on a classical physics concept. - Momentum is the measure of the motion of an object and is represented by the product of an object's mass and its velocity.- The formula for momentum is: \[ p = m \times v \] where: - \( p \) = momentum, - \( m \) = mass, and - \( v \) = velocity.In our exercise:- The electron has a mass of \( 9.11 \times 10^{-31} \text{ kg} \) and moves with a velocity of \( 2.7 \times 10^{6} \text{ m/s} \).- Substituting these values into the momentum formula, we find the electron's momentum is \( 2.46 \times 10^{-24} \text{ kg m/s} \).This momentum is important because it creates a link between particles with mass like electrons and massless particles like photons. Understanding an electron's momentum is the starting point for exploring deeper quantum mechanics concepts.

Photons, unlike electrons, are massless particles, but they also possess momentum.- The momentum of a photon does not rely on mass. Instead, it's connected to the energy and wavelength of the photon.- The formula for a photon's momentum is: \[ p = \frac{h}{\lambda} \] where: - \( p \) = momentum, - \( h \) = Planck's constant, and - \( \lambda \) = wavelength.In this exercise:- We equated the momenta of the electron and the photon since they have been deemed equal.- Thus, the momentum of the photon was also \( 2.46 \times 10^{-24} \text{ kg m/s} \).Using the relationship between momentum and wavelength, we can derive crucial insights into the behavior of particles like photons, even though they lack mass. This demonstrates the wave-particle duality seen in quantum mechanics.

Planck's constant is a fundamental constant in physics, essential in the field of quantum mechanics. - It typically is represented by \( h \) and has a value of \( 6.626 \times 10^{-34} \text{ m}^2 \text{kg/s} \).- It relates the energy of a photon to its frequency through the equation: \[ E = h u \] where: - \( E \) = energy, - \( h \) = Planck's constant, and - \( u \) = frequency.Planck's constant is also crucial for finding the wavelengths in the de Broglie wavelength formula:- The equation connects mass, speed, and momentum through Planck's constant to determine a particle's wavelength.- In the exercise solution, Planck's constant was used to find both the electron's and the photon's wavelengths as: \[ \lambda = \frac{h}{p} \]This fundamental constant ties together concepts of particles behaving both like waves and like discrete entities, a core idea in quantum theory.