Wavelength
The wavelength of electromagnetic radiation is the distance between successive peaks (or troughs) in a wave, often measured in nanometers (nm). In the case of the electromagnetic radiation emitted by magnesium, the wavelength is given as 285.2 nm. This value needs to be converted to meters when performing calculations with the speed of light. To convert from nanometers to meters, remember that 1 nm equals 10⁻⁹ meters. Therefore, \(285.2 \, nm = 285.2 \, \times \, 10^{-9} \, m = 2.852 \, \times \, 10^{-7} \, m\).
Understading wavelength is crucial because it is directly related to the energy and frequency of the wave. Smaller wavelengths correspond to higher energy radiation.
Frequency
Frequency refers to the number of wave cycles that pass a point per second, measured in hertz (Hz). It's a crucial part of understanding electromagnetic radiation.
To find the frequency of magnesium's radiation, we use the equation: \(c = \lambda u\), where \(c\) is the speed of light (\(3.00 \, \times \, 10^8 \, m/s\), \(\lambda\) is the wavelength, and \(u\) is the frequency.
Rearranging for frequency gives us: \(u = \frac{c}{\lambda}\). Substituting the values, \(u = \frac{3.00 \, \times \, 10^8 \, m/s}{2.852 \, \times \, 10^{-7} \, m} \approx 1.052 \, \times \, 10^{15} \, Hz\).
Frequency is directly related to energy, as higher frequencies imply more energetic waves, which is evident in different types of electromagnetic radiation.
Visible Light Spectrum
The visible light spectrum is the range of electromagnetic wavelengths that can be detected by the human eye. It spans from approximately 380 nm to 750 nm. This range includes all the colors seen in a rainbow, with violet having the shortest wavelength and red the longest. It is a small part of the entire electromagnetic spectrum, which ranges from gamma rays to radio waves.
In the exercise, the wavelength of magnesium's radiation, 285.2 nm, is outside the visible range, meaning it falls within the ultraviolet part of the electromagnetic spectrum, which is invisible to the naked eye.
Energy Calculation
Energy calculation in the context of electromagnetic radiation involves finding the energy of a photon. The energy, \(E\), of a photon is directly proportional to its frequency, \(u\), through Planck's formula: \(E = hu\), where \(h\) is Planck’s constant, \(6.626 \, \times \, 10^{-34} \, Js\).
For our magnesium radiation, substituting \(u = 1.052 \, \times \, 10^{15} \, Hz\) yields: \(E = (6.626 \, \times \, 10^{-34} \, Js)(1.052 \, \times \, 10^{15} \, Hz) \approx 6.97 \, \times \, 10^{-19} \, J\).
This energy calculation helps in understanding the magnitude of energy carried by electromagnetic waves and is crucial in fields like spectroscopy and quantum mechanics.
