## Light and the Electromagnetic Spectrum ### Energy from the Sun

Nearly all (99.97%) of the energy we have on Earth comes from the sun. This amounts to an average of 340 joules/second for every square meter of the Earth's surface.

Solar energy is nuclear energy. It comes from the fusion reactions that occur in the sun. In a fusion reaction, two small nuclei merge to form the nucleus of a larger atom. Some mass is converted to energy in the process. Below is a typical fusion reaction. An isotope of hydrogen, deuterium or 2H, combines with another isotope of hydrogen, tritium or 3H, to form helium and a neutron. The deuterium nucleus consists of 1 proton and 1 neutron with an atomic mass of exactly 2.0. Tritium has 1 proton and 2 neutrons (3.0 amu). The helium nucleus has a mass of 3.98 amu and the free neutron is 1.0 amu. In this reaction some mass, 0.02 amu, is converted into energy.

E = mc2 where c, speed of light = 2.998 x 108 m/sec

Remember that the joule (J) is the standard unit of energy. We can convert any other unit of energy into joules or kilojoules (kJ). There are many online conversions programs to help with the calculations. For example 1 joule is equal to 1 (kilogram)(meter)2/(seconds)2.

In the last lecture you saw that sun, like any other hot object, releases its energy in discrete "rays" that have some properties of particles and some properties of waves. We call it electromagnetic radiation. There is a distribution of energies of the radiation that looks similar to distribution of kinetic energies of atoms and molecules within a substance. Most graphs of energy distributions have a similar shape.

Notice that radiation in the visible light range is close to the average energy for the solar spectrum but there is quite a bit of radiation more and less energetic than this.

You radiate energy, too. The radiation from a body of approximately 310 K is in the infrared range.

Electromagnetic radiation is the type of energy that encompasses light, heat, and x-rays. It can be described using a sinusoidal wave model, where the properties of the radiation depend on the wavelength, frequency, and other parameters of the wave. For some purposes, it makes more sense to describe the energy as a stream of light particles called photons, where the energy of the photons is proportional to the frequency of the radiation.

• Amplitude (A): The height of the wave

• Wavelength (λ): The distance between two crests of the wave

• Crest and trough: The highest and lowest points, respectively, of a wave

• Speed of light ( c ): The velocity of radiation as it travels through a vacuum. This quantity is the same for all forms of electromagnetic radiation, from x-rays to light to radio waves, and is constant within a particular transportation medium.The speed of light in vacuum is 2.99792 x 108 m/s. The speed of light in air is only 0.03% slower, and c in either medium is usually just rounded off to 3.00 x 108 m/s.

• Frequency (ν): The number of waves that pass a fixed point per second

• Period (T): The number of seconds it takes for a wave to pass a fixed point • ν = 1/T - The frequency of the wave is the reciprocal of the period.

• λ ν = c (or ν = c/λ) - the product of frequency and wavelength is the speed of light. Alternatively, the frequency of a wave is inversely proportional to the velocity.

• E = hν = hc/λ , where h is the Planck constant, 6.626 x 10-34 - The energy of the radiation is equal to the Plank constant multiplied by the frequency of the radiation.

### The Electromagnetic Spectrum

Although all waves of electromagnetic radiation travel at the speed of light, different types of waves have vastly differing wavelengths, frequencies, and energies. The shorter the wavelength of the radiation, the greater the frequency and the larger the energy. The electromagnetic spectrum ranges from gamma (γ) radiation, which has the shortest wavelength, highest frequency, and greatest energy, to radio waves, which has the longest wavelength and lowest frequency and energy. Ultraviolet light (UV) is divided into three regions:
• UV A, wavelength = 400 - 320 nm
• UV B, wavelength = 320 - 280 nm
• UV C, wavelength = < 280 nm

Visible light is between 750 nm (red) and 400 nm (violet). Remember Roy G. Biv?

Professor Patricia Shapley, University of Illinois, 2012