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Electromagnetic Radiation and the Bohr Atom Worksheet
Light is known to have the wave-like properties of frequency, , and wavelength, . These are illustrated below. The x-axis is a measure of time.
The distance between the peaks is called the wavelength and the number of waves that pass a certain point per unit time is called the frequency. The frequency is expressed in waves/second or 1/seconds or hertz (Hz). As the frequency increases, the wavelength decreases. In electromagnetic radiation, the wavelength and frequency are related by the equation
Where c = the speed of light, , , and . The electromagnetic spectrum is shown below.
Planck recognized that energy is quantized and related the energy of electromagnetic radiation to its frequency.
Where E = energy in Joules, h = Planck’s constant, .
1. Which color of visible light has the shortest wavelength?
2. Which type of electromagnetic radiation has the shortest wavelengths?
3. Which type of electromagnetic radiation has wavelengths slightly longer than visible light?
4. The wavelength of green light is about . What is the frequency of this radiation?
5. What is the wavelength of a photon that has a frequency of ? Give your answer in nanometers and identify the type of radiation this is.
6. For each of the following pairs of quantities, indicate whether they are related directly or indirectly.
(a) energy and wavelength
(b) wavelength and frequency
(c) frequency and energy
7. A classical radio station broadcasts at megahertz, hertz. Find the wavelength of this radiation, in meters, and the energy of one of these photons, in Joules.
8. What is the energy of a photon with a wavelength of ?
Bohr invented the concept of fixed electron energy levels for atoms and applied this concept to the line spectra of elements. He proposed that only certain energy levels are allowed for electrons within the structure of an atom. Electrons are allowed to move between these energy levels. When electrons move up in energy levels, they absorb very specific amounts of energy and when they move down in energy levels, they emit very specific amounts of energy. The energies absorbed when electrons move up correspond to the dark line atomic spectra and the energies emitted when electrons move down correspond to the bright line atomic spectra. The energies absorbed and emitted are measures of the energy difference between the two energy levels. Ionization energy is the energy required to completely remove an electron from an atom. This can be thought of as the transition between the starting energy level and the infinite energy level.
The energy level concept can be illustrated for a hydrogen atom as shown below.
An equation has been developed for calculating the energy of each energy level.
where E is the energy of the energy level, Z is the nuclear charge, and n is the energy level number. Bohr’s model only worked correctly for atoms with a single electron (essentially hydrogen), and therefore, Z is almost always equal to 1.
This equation can be used to find the energy of each energy level in a hydrogen atom and can also be used to find the difference between two energy levels by calculating the energies of the two levels and subtracting.
9. Calculate the energy of energy level 2 in a hydrogen atom.
10. If an electron in a hydrogen atom dropped from n = 4 to n = 2, what energy would be emitted?
11. What is the frequency of the photon emitted in question 10?
12. How much energy would be released as an electron moved from the n = 4 to the n = 3 energy levels in a hydrogen atom?
13. What frequency of light would be emitted in the electron transition mentioned in question 15?
14. What would be the wavelength of light emitted in question 15?
15. What type of light would be emitted in question 15?
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