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When ultraviolet light with a wavelength of 254 nm falls upon a clean metal surface, the stopping potential necessary to terminate the emission of photoelectrons is 0.181 $\mathrm{V}$ . (a) What is the photoelectric threshold wavelength for this metal? (b) What is the work function for the metal?

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A) 264 $\mathrm{nm}$B) 4.68 $\mathrm{eV}$

Physics 102 Electricity and Magnetism

Physics 103

Chapter 28

Photons, Electrons, and Atoms

Electromagnetic Waves

Atomic Physics

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Lectures

02:42

Atomic physics is the field of physics that studies atoms as an isolated system of electrons and an atomic nucleus. It is primarily concerned with the arrangement of electrons around the nucleus and the processes by which these arrangements change. The theory of quantum mechanics, a set of mathematical rules that describe the behaviour of matter and its interactions, provides a good model for the description of atomic structure and properties.

03:50

In atomic physics, the Rutherford-Bohr model or Bohr model or Bohr model of the atom was first proposed by Niels Bohr in 1913. It was the first quantum theory of the atomic structure, applying the principles of quantum mechanics to the hydrogen atom. The Rutherford-Bohr model is a planetary model in which the electron is assumed to revolve around the nucleus in circular orbits. The Rutherford-Bohr model of the atom was based on Max Planck's quantum theory of radiation, which explained the spectrum of blackbody radiation, and Albert Einstein's theory of the photoelectric effect, which explained the origin of the spectrum of line emission from atoms. The Bohr model of the atom was the first to explain the discrete spectrum of hydrogen and how the spectral lines of the hydrogen atom were split into multiple spectral lines in a phenomenon called the fine structure. It introduced the Bohr radius and the concept of quantum levels to explain the discrete nature of the spectrum of the hydrogen atom. The Bohr model of the atom had a significant influence on the development of quantum mechanics, and was instrumental in the development and validation of quantum mechanics.

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all right. So in order to stop the electrons that are emitted from the service of the metal, the stopping potential energy has to be equal to the kinetic energy of the electron is coming out. And the kinetic energy of the electrons is whatever the photonic imparted to them. Minus the work function of that medal And the energy of each photon is given by H C over Lambda. And we're given that stopping potential. I should say stopping potential energy is 0.181 electron volts. Um, actually, let's let's go straight to solving for the work function. Sophie will be equal to H C o ver lander minus e stop. See. So now we just plug the numbers in. In this case, our wavelength is 250 for Nana meters and are stopping potential 0.181 TV. Which is why we expressed H and devious. Well, and this comes out tio 4.71 you be. So this is the answer to part B. It's easier to do part B first and then part, eh? So if we want to know what the threshold wavelength is, that's basically the wave length at which you're on the threshold of being able to eject electrons. And that happens when the energy of the photons is match to the the work function. So we simply excuse me one moment we have that the work function at Threshold is equal to H C over Lambda Thresh over the special wavelength. So we solve this for landed thresh. We found in part B that the work function is 4.71 TV. Yeah, so he substitute that in and we get that this is 263 nana meters.

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