The Photoelectric Effect Flashcards
What is the equation for the energy of a photon?
E = hf
What is the equation for the kinetic energy of electrons?
KE = energy of photon - energy required to remove electron : KE = hf - ϕ, where ϕ is the work function.
What were Lenard’s experimental observations for the photoelectric effect experiment?
- Not all electrons emerged with same KE
- Max KE independent of light intensity, but depends on light frequency
- No electrons emitted if frequency of light is lower than threshold frequency.
What is the equation for total energy of a photon as a particle? What is the relativistic version? What can you conclude from this?
E(total) = KE + m0c^2
Relativistic KE = (γ-1)m0c^2, where γ = (1-(u^2/c^2))^(-1/2)
From this we can conclude that m0 = 0, because it travels at light speed.
What is the equation for the total energy of a photon in terms of momentum?
E^2 = m0c^2)^2 + (pc)^2, where p is momentum.
So for m0 = 0, E = pc = hf
What is the Compton scattering?
When an X-ray photon scatters off a free, stationary electron.
How do you determine the equation for Compton scattering?
User energy conservation and momentum conservation - make a table of energy and momentum of photon and electron before and after the scattering.
What is the energy of the scattered electron?
Ee = sqrt(mc^2)^2 + (pec)^2)
What is the equation for the momentum of the electron squared after the scattering?
pe^2 = p^2 + p’^2 - 2|p|*|p’| * cos(theta)
What do you end up with after substituting in pe^2?
-2|p||p’|c^2 + 2|p|mc^3 - 2|p’|mc^3 = -2|p||p’|cos(theta) * c^2
How do you come to the final equation for the compton scattering after using momentum conservation?
Divide by c^2, and rearrange. Then substitute in p = h/λ and p’ = h/λ’
What is the final equation for compton scattering?
λ’ - λ = h/mc * (1-cos(theta))
What is the value for the compton wavelength?
λc = 2.42*10^-12
Describe the experiment to look at Compton scattering.
X-ray source shoots x-rays at carbon target, and ionization chambers are located at different angles to measure the wavelengths at these specific angles.
