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Physics - Quantum Mechanics - Photons

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Please help with the following problems.

(1) Suppose that a photon has energy of 5 x 10 -19 J. (five times ten to the negative 19th Joule) What's the wavelength of this photon? What is its frequency?

(2) The photon in the above problem strikes a metal plate that has a work function of PHI = 3 x 10 ^ -19 J. What's the maximum kinetic energy of the ejected electrons? What's their maximum speed? (Use mass of an electron is 9.11 x 10^ -31 kg.)

(3) If a photon of λ = 300 nm strikes a metal with PHI= 7 x 10 -19 J,
Will any electrons be ejected? Explain.

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This solution helps with quantum mechanics problems. A Complete, Neat and Step-by-step Solutions to the Problems is provided.

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(1) Suppose that a photon has energy of 5 x 10 -19 J. (five times ten to the negative 19th Joule) What's the wavelength of this photon? What is its frequency?

Energy of a photon is given by E = hf, where h = Planck's constant = 6.63 x 10^ -34, and f = frequency of the photon.

Here, 5 x 10^ -19 = 6.63 x 10^ -34 x f

So, f = 7.54 x 10^14 Hz. ...

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