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$\bullet$ (a) How much energy is needed to ionize a hydrogen atom that is in the $n=4$ state? (b) What would be the wavelength of a photon emitted by a hydrogen atom in a transition from the $n=4$ state to the $n=2$ state?

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$| 487 \mathrm{nm}$

Physics 102 Electricity and Magnetism

Physics 103

Chapter 28

Photons, Electrons, and Atoms

Electromagnetic Waves

Atomic Physics

University of Michigan - Ann Arbor

University of Winnipeg

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.

01:48

A hydrogen atom is in the …

02:13

How much energy is require…

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a. How much energy is need…

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Calculate the energy and t…

05:37

A hydrogen atom in an $n=2…

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A hydrogen atom emits ligh…

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The ion $L$ i $^{2+}$ make…

02:07

What are the (a) energy, (…

01:37

What is the wavelength of …

What is the energy of a ph…

04:20

For an electron in a hydro…

all right. So in hydrogen, the energy associate id with the quantum number and is given by negative 13.6 TV over and squared. And in part a, we were asked how much energy is needed to, um, ionized an electron from the n equals force. They So when the ionizing electron weaken, basically think of it as being removed infinitely far from the hydrogen atom or practically infinite, in which case the energy of the electron is a zero. So basically the energy that we have to put in eyes just equal to the energy that the electron initially had, which for an an equals for quantum stay is given by 13.6 TV over four squared, and this is 0.85 BB. Now, if we have a transition between Orbital's two and four, then we need to take a difference of energies using the same expression. So the energy associate ID with the N equals to orbital is, um, 13.6 TV over one over two squared, and we take the difference with the N equals for orbital and the energy supplied, um, to the photon is given by the difference of these energies. Basically, the change in energy in the orbital's is compensated for by the mission or absorption of the photo, and this comes out to 2.55 If we want to know the wavelength, then we can set the sequel to each C over Lambda with H expressed in electron volts and solving for land gives 487 nano meters, I think.

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