Question 13 Weeks 2-4 Achieve

[alexia11]

The question asks to use the wavelength of the electron to find the energy of the photon. My question is how would the kinetic energy found using c= wavelength x frequency. Be used to find momentum in terms of energy. This portion of the solution for this question confused me.

[Kaija Frassrand 2F]

Start with the kinetic energy equation:
K.E. = (1/2)mv^2

Use the de Broglie wavelength equation to express momentum (p) in terms of the wavelength and Planck's constant:
p = h / λ

Substitute this expression for momentum into the kinetic energy equation:
K.E. = (1/2)m(v^2)

Now, we can express v in terms of λ and f, as c (the speed of light) is equal to λf:
v = fλ

Substitute this expression for v into the kinetic energy equation:
K.E. = (1/2)m(fλ)^2

Simplify the equation:
K.E. = (1/2)m(f^2λ^2)

Now, you have an expression for kinetic energy in terms of the frequency (f) and the wavelength (λ). To find momentum in terms of energy, you can rearrange the equation to solve for momentum (p):
K.E. = (1/2)m(f^2λ^2)
2K.E. = mf^2λ^2
p = h / λ

Now, you have an expression for momentum (p) in terms of kinetic energy (K.E):
p = (2K.E) / (hf)

So, you can use this equation to find the momentum of a particle in terms of its kinetic energy, Planck's constant (h), and the frequency (f) of the associated wave