Atomic Physics• To know the structure of the atom, we must know the

following: • What are the parts of the atom? • How are these parts arranged? • The parts of the atom:

– chemistry and electromagnetism ---> electron (first subatomic particle)

– radioactivity ---> nucleus • proton • neutron

• How the atom is arranged - quantum mechanics puts it all together: – atomic spectra ---> Bohr model of the atom – wave-particle duality ---> Quantum model of the atom

• atom = 1 x 10-10 meters • nucleus = 1 x 10-15 to 1 x 10 -14 meters • neutron or proton = 1 x 10-15 meters • electron - not known exactly, but thought to

be on the order of 1 x 10-18 meters • scanning tunneling microscope

• 28.1 EARLY MODELS OF THE ATOM• In the late 19th century, chemists and physicists were studying

the relationship between electricity and matter. In 1897, a British physicist, J. J. Thomson did a series of experiments and suggested a model of the atom as a volume of positive charge with electrons embedded throughout the volume, much like the seeds in a watermelon (Fig. 28.1).

• Negatively charged electrons were located within a continuous distribution of positive charge.The positive charge was assumed to be spherical shape

of radius 10-10m (This value can be obtained from the density of typical solid material, its atomic weight and Avogadro's number).

- In the lowest energy state the electrons are fixed at their equilibrium positions

- In excited atom at high temperature the electrons vibrate about their equilibrium position in simple harmonic motion

- Later, an American Physicist named Robert Milikan measured the electrical charge of an electron. With these two numbers (charge, charge to mass ratio), physicists calculated the mass of the electron as 9.10 x 10-28 grams.

• Example:If the total positive charge in Thomson's model are distributed uniformly over a sphere of radius 10-10m. Find the force constant k and the frequency of the motion

• Let the magnitude of the +ve charge = e and the radius of the +ve charge is r=10-10m

• This is the radiation emitted by the atom which have wavelength of

• This is the expected radiation from Thomson hydrogen atom.

• Example:Assume that there is one electron of charge -e inside spherical region of uniform positive charge density r (according to Thomson's model). Show that the electron motion is in simple harmonic motion about the centre of the sphere.

• If the electron displaced by distance a (a<r), then the electric force acting on the electron is

The charge q can be found by the density of distribution ρ

let F = - kaThis force will produce simple harmonic motion

along the diameter of the sphere directed toward the centre.

• Example:If the total positive charge in Thomson's model are distributed uniformly over a sphere of radius 10-10m. Find the force constant k and the frequency of the motion.

• Solution:Let the magnitude of the +ve charge = e and the radius

of the +ve charge is r=10-10m

• In 1911 Ernest Rutherford (1871–1937) and his students Hans Geiger and Ernest Marsden performed a critical experiment showing that Thomson’s model couldn’t be correct.

• In this experiment, a beam of positively charged alpha particles was projected against a thin metal foil, as in Figure 28.2a

• The results of the experiment were astounding.• Most of the alpha particles passed through the foil as if it were empty space,• but a few particles deflected from their original direction of travel were scattered through large angles.• Some particles were even deflected backwards,

reversing their direction of travel.• Such large deflections were not expected on the basis

of Thomson’s model because a positively charged alpha particle would never come close enough to a large positive charge to cause any large-angle deflections.

• Rutherford explained these results by assuming that the positive charge in an atom was concentrated in a region that was small relative to the size of the atom.

• He called this concentration of positive charge the nucleus of the atom.

• Any electrons belonging to the atom were assumed to be in the relatively large volume outside the nucleus.

• In order to explain why electrons in this outer region of the atom were not pulled into the nucleus, Rutherford viewed them as moving in orbits about the positively charged nucleus in the same way that planets orbit the Sun, as shown in Figure 28.2b

• There are two basic difficulties with Rutherford’s planetary model

• First, an atom emits certain discrete characteristic frequencies of electromagnetic radiation and no others; the Rutherford model is unable to explain this phenomenon.

• Second, the electrons in Rutherford’s model undergo a centripetal acceleration.

• According to Maxwell’s theory of electromagnetism, centripetally accelerated charges revolving with frequency f should radiate electromagnetic waves of the same frequency. As the electron radiates energy, the radius of its orbit steadily decreases and its frequency of revolution increases. This leads to an ever-increasing frequency of emitted radiation and a rapid collapse of the atom as the electron spirals into the nucleus.

28.2 ATOMIC SPECTRA• Why the hydrogen atom, it’s especially

important, although it is the simplest atomic system1. The quantum numbers used to characterize the

allowed states of hydrogen can also be used to describe (approximately) the allowed states of more complex atoms.

2. The hydrogen atom is an ideal system for performing precise comparisons of theory with experiment and for improving our overall understanding of atomic structure.

3. Much of what is learned about the hydrogen atom with its single electron can be extended to such single-electron ions as He+ and Li2+.

• Suppose an evacuated glass tube is filled with hydrogen (or some other gas) at low pressure. If a voltage applied between metal electrodes in the tube is great enough to produce an electric current in the gas, the tube emits light having a colour that depends on the gas inside. (This is how a neon sign works.)

• When the emitted light is analyzed with a spectrometer, discrete bright lines are observed, each having a different wavelength, or colour. Such a series of spectral lines is commonly called an emission spectrum. The wavelengths contained in such a spectrum are characteristic of the element emitting the light

• no two elements emit the same line spectrum, this phenomenon represents a marvellous and reliable technique for identifying elements in a gaseous substance.

• The emission spectrum of hydrogen shown in Figure 28.4 includes four prominent lines that occur at wavelengths of 656.3 nm, 486.1 nm, 434.1 nm, and 410.2 nm, respectively.

• In 1885 Johann Balmer (1825–1898) found that the wavelengths of these and less prominent lines can be described by the simple empirical equation

28.1• Where n may have integral values of 3, 4, 5, . . . , and

RH is a constant, called the Rydberg constant. If the wavelength is in meters, RH has the value

28.2The first line in the Balmer series, at 656.3 nm,

corresponds to n =3 in Equation 28.1, the line at 486.1 nm corresponds to n = 4a Lyman series was subsequently discovered in the far

ultraviolet

• An element can absorb light at specific wavelengths.

• The spectral lines corresponding to this process form what is known as an absorption spectrum.

• An absorption spectrum can be obtained by passing a continuous radiation spectrum (one containing all wavelengths) through a vapour of the element being analyzed.

• The absorption spectrum consists of a series of dark lines superimposed on the otherwise bright continuous spectrum.

• Each line in the absorption spectrum of a given element coincides with a line in the emission spectrum of the element.

• The absorption spectrum of an element has many practical applications. For example, the continuous spectrum of radiation emitted by the Sun must pass through the cooler gases of the solar atmosphere before reaching the Earth

• A new element had been discovered! Because the Greek word for Sun is helios, the new element was named helium

• A continuum spectrum results when the gas pressures are higher. Generally, solids, liquids, or dense gases emit light at all wavelengths when heated.

• An emission spectra are produced by thin gases in which the atoms do not experience many collisions (because of the low density). The emission lines correspond to photons of discrete energies that are emitted when excited atomic states in the gas make transitions back to lower-lying levels.

• An absorption spectrum occurs when light passes through a cold, dilute gas and atoms in the gas absorb at characteristic frequencies; since the re-emitted light is unlikely to be emitted in the sa

• Applying Physics 28.1 Thermal or Spectral?Explanation A simple determination could be madeby observing the light from the candle flame througha spectrometer, which is a slit and diffraction gratingcombination . If the spectrum of the light is

continuous, then it’s probably thermalin origin. If the spectrum shows discrete lines, it’satomic in origin. The results of the experiment showthat the light is indeed thermal in origin and

originates:from random molecular motion in the candleflame.

• Applying Physics 28.2 AurorasExplanation The aurora is due to high speed particlesinteracting with the Earth’s magnetic field andentering the atmosphere. When these particles collidewith molecules in the atmosphere, they excite themolecules in a way similar to the voltage in thespectrum tubes discussed earlier in this section. Inresponse, the molecules emit colors of light accordingto the characteristic spectrum of their atomicconstituents. For our atmosphere, the primaryconstituents are nitrogen and oxygen, which providethe red, blue, and green colors of the aurora