Conceptual Physics

Step-by-step solution

Step Reason

1. E = hf energy of photon

2. frequency, wave speed and wavelength

3. substitute equation 2 into equation 1

4. energy difference

5. substitute equation 4 into equation 3

6. evaluate

36.22 - Gotchas

An atom’s electrons can exist at any energy level. No, this statement contradicts one of the key tenets of quantum physics. The electrons can only exist at specific energy states, and will not be found with energies between those levels. A friend says: an electron falls from an energy level of í4.5 eV to í7.2 eV. It emits a photon with 2.7 eV of energy. Has he learned his quantum physics? Yes, he has. The energy of the photon equals the amount of energy given up by the atom. All photons have the same energy. No, all photons of electromagnetic radiation (for example, light) of a particular frequency have the same amount of energy. The energy of a photon increases with the frequency of the radiation.

36.23 - Summary

Something is quantized if it has a smallest, indivisible unit. The opposite of quantized is continuous. The eggs you buy in a carton at the grocery store are quantized; the amount of milk you pour into a glass is effectively continuous. The Balmer series formula predicts the wavelengths of visible light that are present in the emission spectrum of excited hydrogen gas. When discovered, it revealed a mathematical pattern in the spacing of the spectral emission (or absorption) lines of hydrogen that strongly hinted at an underlying order. The physicists Max Planck and Albert Einstein showed that radiation is quantized. The quantum of light is called a photon. The energy of a photon of electromagnetic radiation equals Planck’s constant times the frequency of the radiation. Einstein cleared up the mystery behind the photoelectric effect by making the assumption that light is quantized.

Niels Bohr developed the basis for the modern-day quantum view of the atom. He stated that the orbits of electrons around the nucleus of an atom are quantized: Electrons can only exist at orbits of specific radii and energy levels. When its electrons jump between levels, an atom emits or absorbs photons whose energy corresponds to the change in electron energy.

Quantum theory is used in the design of semiconductors. Semiconductors are doped í mixed with impurities í to alter the nature of the resistance they offer to currents. Doping creates more mobile electrons and holes than exist in pure semiconductor material.

Key components of transistors include p- and n-type semiconductors. A p-type material has mobile holes that act as charge carriers; an n-type material has mobile electrons. An external potential difference can increase the supply of these charge carrriers near a p-n junction in a transistor, allowing current to flow more readily. However, if the potential difference is changed in magnitude or reversed, it can cause mobile charge carriers to move away from the junction, reducing the flow of current or stopping it altogether. Laser designers also rely on insights from quantum theory. Some agent such as an electrical discharge excites the laser medium, for example a helium-neon gas mixture. This elevates the medium’s electrons to higher energy states. When photons of light are injected into the medium, the excited atoms are stimulated to emit identical, in-phase photons, increasing the flux of photons in the medium and amplifying the light.

For a laser to work, there must be a population inversion: there must be more excited atoms than unexcited ones in the laser medium. If there is no population inversion, then any photons injected into the medium will be absorbed, increasing the energy of the atoms, rather than causing additional photons to be emitted.

Balmer series

Energy of electromagnetic radiation

E = hf (one photon)

E = nhf (multiple photons)