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$\bullet$ Find the wavelengths of a photon and an electron that have the same energy of 25 $\mathrm{eV}$ . (The energy of the electron is its kinetic energy.)

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0.2454 $\mathrm{nm}$

Physics 102 Electricity and Magnetism

Physics 103

Chapter 28

Photons, Electrons, and Atoms

Electromagnetic Waves

Atomic Physics

Rutgers, The State University of New Jersey

University of Michigan - Ann Arbor

Simon Fraser University

McMaster University

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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Calculate the wavelength …

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An electron and a photon e…

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A photon of green light ha…

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For an electron in a hydro…

Okay, So for this problem, we want to get the wave lines. But photo on electron that have 25 b. Um and so Hee is equal to 25 e v and the energy of photons. This is kind of interesting questions. So And you were photon generals, HC over Lambda said that our land, uh, which I was kind of a little subheading Proton, Lando's HC over e. And then if I take this e convert it to E V well and then use my age of 6.626 10 minus three and then see 3 28 Let's see what I got. So each see departed by 25 You Oh, my God. Were 97 ton of minus eight meters mn for an electron we have Landa is equal Thio h overpay is equal to eight eso kinetic energy. This is a little side calculation up here. Is he squared over two AM So, um so putting pee in terms of kinetic energy, it's gonna be the square root of two m times a kinetic energy. And that's why I'm gonna go ahead and put that into a calculator using massive an electron 9 11 10 miles. 31. And let's see what I got. I'm kind of curious, actually. Let me see. I'm gonna guess I think the electron is gonna have a much smaller reap length, just based on my intuition. Um, Right, Let's find out. So we still need this H on top. Don't need this speed of light. Um, so two crimes line bring toe lovin. Um, I started one when you could buy. Okay, great. So I got 2.45 ton of minus 10. Um, I was 10. So, too far off from each other, but certainly not equal or anything. Is there anything else to that question?

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