1 - Radiating Objects (Thermal or Blackbody Radiation )

All heated objects emit electromagnetic radiation via a continuous distribution of wavelengths. It is beneficial to think of objects as solid objects given that gases behave actually in a different way. Liquids can be even even more complicated. In certain, a gas consisting of atoms of a offered type emit discrete wavelengths (or frequencies) of electromagnetic radiation. We have the right to understand, at least roughly, why gases and also solids need to be different in this respect. Gases consist of individual atoms (or molecules) much apart from each other. So the radiation from a gas is simply the radiation from individual atoms. However, a solid is made of very closely packed atoms (or molecules) which affect each other"s properties. Hence, the radiation from a solid is NOT the radiation from single atoms yet the radiation that results from a facility connected system of atoms.

The wavelength equivalent to the maximum intensity of radiation depends inversely on the object"s temperature. Notice in Figure 22-14 where the high suggest on the curve occurs and exactly how this relies on temperature.

The complete power radiated boosts rapidly via temperature. Again, look at the curves in Figure 22-14. Notice just how a element of 2 in the temperature results in a a lot larger readjust in the intensity or brightness.

The spectrum of thermal or blackbody radiation is very equivalent for all objects at the same temperature; i.e., it is the same for most products. This is a profound conclusion, and it was Planck that uncovered the precise formula for describing this spectrum. As stated previously, he designed "quantum oscillators," the atoms that emit and absorb the observed radiation. Planck"s oscillators have actually quantized energies, just as Bohr orbits in an atom have quantized energies. The permitted energies of the oscillator are E = nhf, wbelow n is an integer, h is Planck"s continuous, and f if the frequency connected via the oscillator. (Note his oscillators can take on any frequency.) The quantization aspect of Planck"s led to the correct summary of the thermal radiation spectrum.

Example: What frequency is required to create quanta through energies of 1 eV (electron volts)?

Keep in mind that 1 eV is the kinetic energy gained by an electron or a proton acted upon by a potential difference of 1 volt.

The formula for power in regards to charge and also potential distinction is E = QV. So 1 eV = (1.6 x 10^-19 coulombs)x(1 volt) = 1.6 x 10^-19 Joules.

Now let"s calculate the frequency of the 1 eV photon. E = hf, so f = E/h. Hence, f = 1 eV/6.63 x 10-34 Joule-sec x (1.6 x 10-19 Joule / 1 eV) = 2.41 x 1014 sec-1 or 2.41 x 1014 Hz ( Hz indicates 1/sec). This frequency is in the infrared range, so we can not view these photons with our eyes. Keep in mind exactly how we multiplied by the convariation aspect in between Joules and eV to make those devices cancel so that we could expush the answer in inverse seconds.

2 - More About the Photoelectrical Effect

Here we testimonial vital points about the photoelectric effect and also offer a numerical instance based on Einstein"s formula. The photoelectrical impact is checked out to have actually the adhering to properties:

Light shined on some metals emits electrons. Electrons are ejected immediately...there is no substantial delay. The circulation of energies of emitted electrons does not depfinish on the intensity of the light. Whether electrons are emitted at all relies on the frequency of the light being high sufficient. The maximum kinetic power depends only on the frequency of the light.

The timeless wave concept can not define all these facts. For instance, one would certainly intend in the classical theory that incredibly low intensity light would not eject electrons as quickly as high intensity light. Classically, emitting electrons would take place in the same method that water molecules acquire boiled away...i.e., the hotter (even more intense) the flame, the much faster the boiling. Also, one might intend that the higher the intensity of the radiation, the even more energy that might be transmitted to a provided electron, and that the circulation of energies would certainly depfinish on the intensity. It does not make sense, classically, for tbelow to be a minimum frequency for electrons to be emitted at all...or that the maximum kinetic energy of an electron depends on the frequency of the light.

Einstein"s concept that light consists of bundles of energy, pholoads, makes sense for explaining the photoelectrical effect. Here is what he concluded. The maximum energy of an emitted electron is equal to the power of a photon for frequency f (i.e., E = hf ), minus the power forced to eject an electron from the metal"s surface (the so-dubbed work function). This states that it takes only one photon to eject an electron, so the intensity of photons (or the intensity of light) is not the key aspect if the power of not among the photons is good enough. If the power of a solitary photon is given by E = hf, we check out just how it counts on the frequency, f. For an electron to be ejected from the surchallenge of a metal, enough power need to be used to break its bond with the atom from which it originates...therefore, the occupational attribute.

You deserve to obtain an excellent description of the photoelectric result from the Colorado"s Physics 2000 Webwebsite.

Example: What is the maximum kinetic power of an emitted electron if light via a frequency of 2 x 1015 shines on Aluminum via a work-related feature (phi) = 4.08 eV?

K.E.(max) = hf - phi = (4.14 x 10-15 eV-sec) x ( 2 x 1015 Hz ) - 4.08 eV = 4.2 eV

Note: h = 6.63 x 10-34 J-s x ( 1 eV / 1.6 x 10-19 Joules) = 4.14 x 10-15 eV-s

3 - Bohr"s Atom: The Rutherford Atom With the Quantum Hypothesis Added

Planck"s formula described the thermal spectrum of solid objects. Bohr"s picture of the atom described the discrete energies (colors) seen when hydrogen gas is heated. It likewise described in much less exact detail, however in a qualitatively correct means the spectra observed for other atoms.

Bohr"s photo of the atom begins through the Rutherford model of a minature planetary device obeying classic mechanics, wright here electrons are choose planets executing circular orbits around the nucleus. Bohr adds three key postulates to the Rutherford model.

Orbits are discrete, and also the angular momentum of each orlittle is offered by L = nh/2pi, where n = 1, 2, 3, and so on, h is Planck"s constant, and also pi = 3.1416. Electrons don"t radiate repetitively, as the rules of classic electromagnetism need. This is a postulate of Bohr"s. He doesn"t define why. That comes later. Photons are emitted or took in as electrons jump from a greater to a reduced orlittle bit, respectively.

The radii of the unique orbits in the Bohr Model are given by the formula r(n) = r(1)n2, wright here n = 1, 2, 3, ..., and so on, and also r(1) = 5.31 x 10^-11 meters, wright here r(1) is the radius of the first Bohr orlittle bit and also r(n) is the radius of orbit number n.

The Energies of the electrons in the assorted Bohr orbits is provided by E(n) = -13.6 eV / n2 ; wbelow n = 1, 2, 3, ..., and so on.

4 - Atomic Spectra

The Bohr picture describes the emission and also absorption spectra of hydrogen, and also hydrogen-favor atoms superbly well. Hydrogen-prefer atoms are those wright here tright here is only one electron outside of a core that consists of the atom"s nucleus and "closed shells" of electrons. In other words, the outer electron "sees" a net central positive charge (made of the nuclear charge and the charge of all the inner electrons) about which it orbits...and in this sense it behave choose hydrogen through one electron orbiting a single positive charge, a proton.

Emission Spectra are created by photons through discrete frequencies f, wbelow, f = deltaE/h. deltaE is the power distinction in between the energies of an electron in a higher orlittle jumping to a lower orbit.

Absorption Spectra the lacking discrete frequencies in a continuous spectrum which outcomes from pholots of special energies being absorbed from the light by an intervening gas. The atoms in the gas aborb pholoads through precisely the appropriate energies (or wavelengths) to make an electron in that atom jump from a lower to a greater orlittle.

Recheck out Figures 22-2 and 22-3 in the text which display emission and absorption spectra.

Example: As an electron drops from the mth to the nth level in the Bohr atom E(m) - E(n) = -13.6 eV/m2 - -13.6 eV/n2 = -13.6 eV ( 1/m2 - 1/n2 ) For transition from 2 --> 1 levels E(2) - E(1) = -13.6 eV ( 1/22 - 1/12 ) = 3/4 (13.6 eV) = 10.2 eV. The frequency of emitted pholoads is given by f = E/h = 10.2 eV / 6.63 x 10-34 J-sec x ( 1.6 x 10-19 J / 1 eV ) = 2.46 x 1015 Hz (Ultraviolet).

R.S. Panvini 2/19/2003