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Light wavelength and photoelectrons

Problem 1. With light of wavelength 520 nm, photoelectrons are ejected from a metal surface with a maximum speed of 1.78 x 10^5 m/s.
a) What wavelength would be needed to vie a maximum speed of 4.81 x 10^5 m/s?
b) Can you guess what metal it is?

Problem 2. In positron emission tomography an electron and positron annihilate, and two photons of the same energy are detected. What is the energy and the wavelength of the photon? The electron-positron pair can be assumed stationary before the annihilation.

Problem 3. The Compton scattering.
Suppose a photo scatters off of a free proton. What is the maximum possible change of the wavelength?

Problem 4. Doubly ionized lithium, Li^2+, absorbs a photon and jumps from the ground state to its n = 3 level. What was the wavelength of the photon?

Bonus Question. All other things being equal, which would be more likely to exhibit its wave nature - a proton or an electron - and why?

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The expert examines light wavelength and photoelectrons. The positron emisson tomography for an electron and positron annihilate is determined.

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