## Homework 1.33

$c=\lambda v$

Essly Mendoza 1J
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### Homework 1.33

Question 33 reads the velocity of an electron that is emitted from a metallic surface by a photon is 3.6x10^3 km s^-1. a) What is the wavelength of the ejected electron? b) No electrons are emitted from the surface of the metal until the frequency of the radiation reaches 2.50 x10^16 Hz. how much energy is required to remove the electron from the metal surface? c) What is the wavelength of the radiation caused photoejection of the electron? d) What kind of electromagnetic radiation was used?

Does anyone know how to go about part c? The frequency was given 2.50 x 10^16 Hz, but I'm under the impression that I can't just use the formula wavelength= c/v, so how can I find the wavelength in this case then? thanks guys!

Chem_Mod
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### Re: Homework 1.33

Use the photoelectric effect equation (deciding to use this equation can be hinted from the fact that we're dealing with photoejection of electrons). Work function would equal your answer in part b. Ek can be calculated by using the velocity given in the first sentence. Add these two energy quantities to get the energy of the light that shines on the metal plate. You can then use Elight = $\frac{h*c}{\lambda}$ to find wavelength.

Austin Ho 1E
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### Re: Homework 1.33

Part (c) asks about the wavelength of light required to remove the electron at the speed given (3.6*10^3 km/s). This is important, as you must use the photoelectric effect equation that relates Kinetic Energy to the energy of the photon and the work function.

The equation gives us: 1/2*mass of the electron*velocity of electron^2 = Planck's constant*frequency of photon - work function. Since you already solved for the work function in the previous example (through E=hv), it's just a matter of plugging in values and rearranging.

Since they're asking for wavelength that ejects the electron at that speed, I converted the term (Planck's constant*frequency of photon) to (Planck's constant*speed of light/wavelength of photon).
Thus we get: 1/2*mass of the electron*velocity of electron^2 = Planck's constant*speed of light/wavelength of photon - work function
By rearranging, we find that: Wavelength = h*c/(1/2*m*v^2 + work function). From there, just plug in values.

Hope that helps!