Atomic physics

Сентябрь 2, 2022

Содержание

2. Physical Interpretation of the Quantum Numbers The Orbital Quantum Number l According to quantum mechanics, an
3. Physical Interpretation of the Quantum Numbers The Orbital Magnetic Quantum Number ml
4. Physical Interpretation of the Quantum Numbers The Orbital Magnetic Quantum Number ml A vector model that
5. Physical Interpretation of the Quantum Numbers The Orbital Magnetic Quantum Number ml
6. Physical Interpretation of the Quantum Numbers The Spin Magnetic Quantum Number ms Electron spin
7. Because spin is a form of angular momentum, it must follow the same quantum rules as
8. Physical Interpretation of the Quantum Numbers The Spin Magnetic Quantum Number ms
9. Physical Interpretation of the Quantum Numbers The Spin Magnetic Quantum Number ms
10. The Exclusion Principle and the Periodic Table For our discussion of atoms with many electrons, it
11. The Exclusion Principle and the Periodic Table The filling of electronic states must obey both the
12. The Exclusion Principle and the Periodic Table Hund’s rule, states that when an atom has orbitals
13. The Exclusion Principle and the Periodic Table The periodic table
14. The Exclusion Principle and the Periodic Table Ionization energy of the elements versus atomic number
15. More on Atomic Spectra: Visible and X-Ray Transitions for which l does not change are very
16. More on Atomic Spectra: Visible and X-Ray The selection rules for the allowed transitions are the
17. More on Atomic Spectra: Visible and X-Ray X-Ray Spectra X-rays are emitted when high-energy electrons or
18. More on Atomic Spectra: Visible and X-Ray X-Ray Spectra Figure shows a machine that uses a
19. X-Ray Spectra More on Atomic Spectra: Visible and X-Ray Other characteristic x-ray lines are formed when
20. More on Atomic Spectra: Visible and X-Ray X-Ray Spectra We can now estimate the energy associated
21. More on Atomic Spectra: Visible and X-Ray X-Ray Spectra A Moseley plot of !1/l versus Z,
22. Spontaneous and Stimulated Transitions This process is called stimulated absorption because the photon stimulates the atom
23. Spontaneous and Stimulated Transitions Once an atom is in an excited state, the excited atom can
24. Spontaneous and Stimulated Transitions In addition to spontaneous emission, stimulated emission occurs. In this process, the
25. Lasers The primary properties of laser light that make it useful in these technological applications are
26. Lasers We have described how an incident photon can cause atomic energy transitions either upward (stimulated
27. Lasers For the stimulated emission to result in laser light, there must be a buildup of
28. Lasers • The emitted photons must be confined in the system long enough to enable them
29. Lasers One device that exhibits stimulated emission of radiation is the helium–neon gas laser. Figure is
30. Lasers Applications This robot carrying laser scissors, which can cut up to 50 layers of fabric
31. Lasers Applications An optical trap for atoms is formed at the intersection point of six counterpropagating
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Слайд 2

Physical Interpretation of the Quantum Numbers
The Orbital Quantum Number l
According to

quantum mechanics, an atom in a state whose principal quantum number is n can take on the following discrete values of the magnitude of the orbital angular momentum:

Слайд 3

Physical Interpretation of the Quantum Numbers
The Orbital Magnetic Quantum Number ml

Слайд 4

Physical Interpretation of the Quantum Numbers
The Orbital Magnetic Quantum Number ml
A

vector model that describes space quantization for the case l=2.

Слайд 5

Physical Interpretation of the Quantum Numbers
The Orbital Magnetic Quantum Number ml

Слайд 6

Physical Interpretation of the Quantum Numbers
The Spin Magnetic Quantum Number ms
Electron

spin

Слайд 7

Because spin is a form of angular momentum, it must follow

the same quantum rules as orbital angular momentum. Te magnitude of the spin angular momentum for the electron is

Physical Interpretation of the Quantum Numbers

The Spin Magnetic Quantum Number ms

Слайд 8

Physical Interpretation of the Quantum Numbers
The Spin Magnetic Quantum Number ms

Слайд 9

Physical Interpretation of the Quantum Numbers
The Spin Magnetic Quantum Number ms

Слайд 10

The Exclusion Principle and the Periodic Table
For our discussion of atoms

with many electrons, it is often easiest to assign the quantum numbers to the electrons in the atom as opposed to the entire atom. An obvious question that arises here is, “How many electrons can be in a particular quantum state?” Pauli answered this important question in 1925, in a statement known as the exclusion principle:

No two electrons can ever be in the same quantum state; therefore, no two electrons in the same atom can have the same set of quantum numbers.

Слайд 11

The Exclusion Principle and the Periodic Table
The filling of electronic states

must obey both the exclusion principle and Hund’s rule

Слайд 12

The Exclusion Principle and the Periodic Table
Hund’s rule, states that
when

an atom has orbitals of equal energy, the order in which they are filled by electrons is such that a maximum number of electrons have unpaired spins.

Слайд 13

The Exclusion Principle and the Periodic Table
The periodic table

Слайд 14

The Exclusion Principle and the Periodic Table
Ionization energy of the elements

versus atomic number

Слайд 15

More on Atomic Spectra: Visible and X-Ray
Transitions for which l does

not change are very unlikely to occur and are called forbidden transitions. (Such transitions actually can occur, but their probability is very low relative to the probability of “allowed” transitions.) The various diagonal lines represent allowed transitions between stationary states. Whenever an atom makes a transition from a higher energy state to a lower one, a photon of light is emitted.

Слайд 16

More on Atomic Spectra: Visible and X-Ray
The selection rules for the

allowed transitions are

the allowed energies for one-electron atoms and ions, such as hydrogen and He+ are

This equation was developed from the Bohr theory, but it serves as a good first approximation in quantum theory as well.

Слайд 17

More on Atomic Spectra: Visible and X-Ray
X-Ray Spectra
X-rays are emitted when

high-energy electrons or any other charged particles bombard a metal target. The x-ray spectrum typically consists of a broad continuous band containing a series of sharp lines.

X-ray radiation with its origin in the slowing down of electrons is called bremsstrahlung, the German word for “braking radiation.”

The discrete lines called characteristic x-rays.

Слайд 18

More on Atomic Spectra: Visible and X-Ray
X-Ray Spectra
Figure shows a machine

that uses a linear accelerator to accelerate electrons up to 18 MeV and smash them into a tungsten target. The result is a beam of photons, up to a maximum energy of 18 MeV, which is actually in the gamma-ray range. This radiation is directed at the tumor in the patient.

Слайд 19

X-Ray Spectra
More on Atomic Spectra: Visible and X-Ray
Other characteristic x-ray lines

are formed when electrons drop from upper levels to vacancies other than those in the K shell. For example, L lines are produced when vacancies in the L shell are filled by electrons dropping from higher shells. An Lα line is produced as an electron drops from the M shell to the L shell, and an Lβ line is produced by a transition from the N shell to the L shell.

Слайд 20

More on Atomic Spectra: Visible and X-Ray
X-Ray Spectra
We can now estimate

the energy associated with an electron in the L shell:

After the atom makes the transition, there are two electrons in the K shell. We can approximate the energy associated with one of these electrons as that of a one-electron atom. (In reality, the nuclear charge is reduced somewhat by the negative charge of the other electron, but let’s ignore this effect.) Therefore,

Слайд 21

More on Atomic Spectra: Visible and X-Ray
X-Ray Spectra
A Moseley plot of

!1/l versus Z, where λ is the wavelength of the Kα x-ray line of the element of atomic number Z.

From this plot, Moseley determined the Z values of elements that had not yet been discovered and produced a periodic table in excellent agreement with the known chemical properties of the elements. Until that experiment, atomic numbers had been merely placeholders for the elements that appeared in the periodic table, the elements being ordered according to mass.

Слайд 22

Spontaneous and Stimulated Transitions
This process is called stimulated absorption because the

photon stimulates the atom to make the upward transition.

Слайд 23

Spontaneous and Stimulated Transitions
Once an atom is in an excited state,

the excited atom can make a transition back to a lower energy level, emitting a photon in the process. This process is known as spontaneous emission because it happens naturally, without requiring an event to trigger the transition. Typically, an atom remains in an excited state for only about 10-8 s.

Слайд 24

Spontaneous and Stimulated Transitions
In addition to spontaneous emission, stimulated emission occurs.

In this process, the incident photon is not absorbed; therefore, after the stimulated emission, two photons with identical energy exist: the incident photon and the emitted photon.

Слайд 25

Lasers
The primary properties of laser light that make it useful in

these technological applications are the following:
• Laser light is coherent. The individual rays of light in a laser beam maintain a fixed phase relationship with one another.
• Laser light is monochromatic. Light in a laser beam has a very narrow range of wavelengths.
• Laser light has a small angle of divergence. The beam spreads out very little, even over large distances.

Слайд 26

Lasers
We have described how an incident photon can cause atomic energy

transitions either upward (stimulated absorption) or downward (stimulated emission). The two processes are equally probable. When light is incident on a collection of atoms, a net absorption of energy usually occurs because when the system is in thermal equilibrium, many more atoms are in the ground state than in excited states. If the situation can be inverted so that more atoms are in an excited state than in the ground state, however, a net emission of photons can result. Such a condition is called population inversion. Population inversion is, in fact, the fundamental principle involved in the operation of a laser (an acronym for light amplification by stimulated emission of radiation). The full name indicates one of the requirements for laser light: to achieve laser action, the process of stimulated emission must occur.

Слайд 27

Lasers
For the stimulated emission to result in laser light, there must

be a buildup of photons in the system. The following three conditions must be satisfied to achieve this buildup:
• The system must be in a state of population inversion: there must be more atoms in an excited state than in the ground state. That must be true because the number of photons emitted must be greater than the number absorbed.
• The excited state of the system must be a metastable state, meaning that its lifetime must be long compared with the usually short lifetimes of excited states, which are typically 1028 s. In this case, the population inversion can be established and stimulated emission is likely to occur before spontaneous emission.

Слайд 28

Lasers
• The emitted photons must be confined in the system long

enough to enable them to stimulate further emission from other excited atoms. That is achieved by using reflecting mirrors at the ends of the system. One end is made totally reflecting, and the other is partially reflecting. A fraction of the light intensity passes through the partially reflecting end, forming the beam of laser light.

Слайд 29

Lasers
One device that exhibits stimulated emission of radiation is the helium–neon

gas laser. Figure is an energy-level diagram for the neon atom in this system. The mixture of helium and neon is confined to a glass tube that is sealed at the ends by mirrors. A voltage applied across the tube causes electrons to sweep through
the tube, colliding with the atoms of the gases and raising them into excited states. Neon atoms are excited to state E3* through this process (the asterisk indicates a metastable state) and also as a result of collisions with excited helium atoms. Stimulated emission occurs, causing neon atoms to make transitions to state E2. Neighboring excited atoms are also stimulated. The result is the production of coherent light at a wavelength of 632.8 nm.

Слайд 30

Lasers
Applications
This robot carrying laser scissors, which can cut up to 50

layers of fabric at a time, is one of the many applications of laser technology.

Слайд 31

Lasers
Applications
An optical trap for atoms is formed at the intersection point

of six counterpropagating laser beams along mutually perpendicular axes.

Atomic physics

Содержание

Physical Interpretation of the Quantum NumbersThe Orbital Quantum Number lAccording to

Physical Interpretation of the Quantum NumbersThe Orbital Magnetic Quantum Number ml

Physical Interpretation of the Quantum NumbersThe Orbital Magnetic Quantum Number mlA

Physical Interpretation of the Quantum NumbersThe Orbital Magnetic Quantum Number ml

Physical Interpretation of the Quantum NumbersThe Spin Magnetic Quantum Number msElectron

Because spin is a form of angular momentum, it must follow

Physical Interpretation of the Quantum NumbersThe Spin Magnetic Quantum Number ms

Physical Interpretation of the Quantum NumbersThe Spin Magnetic Quantum Number ms

The Exclusion Principle and the Periodic TableFor our discussion of atoms

The Exclusion Principle and the Periodic TableThe filling of electronic states

The Exclusion Principle and the Periodic TableHund’s rule, states that when

The Exclusion Principle and the Periodic TableThe periodic table

The Exclusion Principle and the Periodic TableIonization energy of the elements

More on Atomic Spectra: Visible and X-RayTransitions for which l does

More on Atomic Spectra: Visible and X-RayThe selection rules for the

More on Atomic Spectra: Visible and X-RayX-Ray SpectraX-rays are emitted when

More on Atomic Spectra: Visible and X-RayX-Ray SpectraFigure shows a machine

X-Ray SpectraMore on Atomic Spectra: Visible and X-RayOther characteristic x-ray lines

More on Atomic Spectra: Visible and X-RayX-Ray SpectraWe can now estimate

More on Atomic Spectra: Visible and X-RayX-Ray SpectraA Moseley plot of

Spontaneous and Stimulated TransitionsThis process is called stimulated absorption because the

Spontaneous and Stimulated TransitionsOnce an atom is in an excited state,

Spontaneous and Stimulated TransitionsIn addition to spontaneous emission, stimulated emission occurs.

LasersThe primary properties of laser light that make it useful in

LasersWe have described how an incident photon can cause atomic energy

LasersFor the stimulated emission to result in laser light, there must

Lasers• The emitted photons must be confined in the system long

LasersOne device that exhibits stimulated emission of radiation is the helium–neon

LasersApplicationsThis robot carrying laser scissors, which can cut up to 50

LasersApplicationsAn optical trap for atoms is formed at the intersection point

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Physical Interpretation of the Quantum Numbers
The Orbital Quantum Number l
According to

Physical Interpretation of the Quantum Numbers
The Orbital Magnetic Quantum Number ml

Physical Interpretation of the Quantum Numbers
The Orbital Magnetic Quantum Number ml
A

Physical Interpretation of the Quantum Numbers
The Orbital Magnetic Quantum Number ml

Physical Interpretation of the Quantum Numbers
The Spin Magnetic Quantum Number ms
Electron

Physical Interpretation of the Quantum Numbers
The Spin Magnetic Quantum Number ms

Physical Interpretation of the Quantum Numbers
The Spin Magnetic Quantum Number ms

The Exclusion Principle and the Periodic Table
For our discussion of atoms

The Exclusion Principle and the Periodic Table
The filling of electronic states

The Exclusion Principle and the Periodic Table
Hund’s rule, states that
when

The Exclusion Principle and the Periodic Table
The periodic table

The Exclusion Principle and the Periodic Table
Ionization energy of the elements

More on Atomic Spectra: Visible and X-Ray
Transitions for which l does

More on Atomic Spectra: Visible and X-Ray
The selection rules for the

More on Atomic Spectra: Visible and X-Ray
X-Ray Spectra
X-rays are emitted when

More on Atomic Spectra: Visible and X-Ray
X-Ray Spectra
Figure shows a machine

X-Ray Spectra
More on Atomic Spectra: Visible and X-Ray
Other characteristic x-ray lines

More on Atomic Spectra: Visible and X-Ray
X-Ray Spectra
We can now estimate

More on Atomic Spectra: Visible and X-Ray
X-Ray Spectra
A Moseley plot of

Spontaneous and Stimulated Transitions
This process is called stimulated absorption because the

Spontaneous and Stimulated Transitions
Once an atom is in an excited state,

Spontaneous and Stimulated Transitions
In addition to spontaneous emission, stimulated emission occurs.

Lasers
The primary properties of laser light that make it useful in

Lasers
We have described how an incident photon can cause atomic energy

Lasers
For the stimulated emission to result in laser light, there must

Lasers
• The emitted photons must be confined in the system long

Lasers
One device that exhibits stimulated emission of radiation is the helium–neon

Lasers
Applications
This robot carrying laser scissors, which can cut up to 50

Lasers
Applications
An optical trap for atoms is formed at the intersection point