Aim: How can we apply mathematics to the photoelectric effect? In the photoelectric effect, how do you increase: The number of ejected electrons? The KE.

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Aim: How can we apply mathematics to the photoelectric effect? In the photoelectric effect, how do you increase: The number of ejected electrons? The KE of the ejected electrons? Increase intensity of the wave Increase frequency of the wave

ome/animations3/modernPhysics/photoele ctricEffect.html

Wave-Particle Duality According to Einstein, light has particle characteristics Light travels as a photon Photon – A “bundle” or “packet” of energy Has zero rest mass but has momentum and energy Albert Einstein 1879 – 1955

Momentum Previously learned p = mv You need mass to have momentum Photons have no mass but have momentum Contradicts classical physics!

The Planck Hypothesis In 1900, Max Planck proposed that energy could exist only in discrete quanta which were proportional to the frequency. Max Planck

= E photon = energy of a photon measured in J or eV

frequency max KE of ejected electrons fofo Slope = h

Also….

How much energy does a photon of yellow light have? E photon = hf E photon = (6.63 x J·s)(5.20 x Hz) E photon = 3.45 x J How many electrons will be ejected if the threshold frequency is 6.20 x Hz? None – If the frequency is below the threshold frequency, no electrons get ejected

Minimum Energy The minimum frequency gives the minimum energy Minimum frequency = threshold frequency (f o ) Minimum energy = work function (W o ) Can you figure out the formula for work function? W o = hf o

What is the work function of zinc if the threshold frequency is 9.6 x Hz? W o = hf o W o = (6.63 x J·s)(9.6 x Hz) W o = 6.4 x J

KE Model for the Ejected Photoelectrons e-e- e-e- e-e- e-e- e-e- e-e- Photon Photoelectrons E photon = hf W o = hf o KE max

Formula KE max = E photon – W o KE max = hf – hf o KE max = h(f – f o )

Light with a frequency of 4.5 x Hz strikes zinc whose work function is 6.4 x J. What is the maximum kinetic energy of the ejected electrons? KE max = hf – W o KE max = (6.63 x J·s)(4.5 x Hz) – 6.4 x J KE max = 3.0 x – 6.4 x KE max = 2.34 x J

The work function of chromium is 4.6 eV. If a photon with 5.0 eV of energy strikes chromium, what is the maximum kinetic energy of the ejected electrons? KE max = E photon – W o KE max = 5.0 eV – 4.6 eV KE max = 0.4 eV Convert this to Joules.