Unfortunately, scientists had not yet developed any theoretical justification for an equation of this form. In , a Danish physicist, Niels Bohr —; Nobel Prize in Physics, , proposed a theoretical model for the hydrogen atom that explained its emission spectrum. Using classical physics, Niels Bohr showed that the energy of an electron in a particular orbit is given by. In that level, the electron is unbound from the nucleus and the atom has been separated into a negatively charged the electron and a positively charged the nucleus ion.
In this state the radius of the orbit is also infinite. The atom has been ionized. In his final years, he devoted himself to the peaceful application of atomic physics and to resolving political problems arising from the development of atomic weapons.
As n decreases, the energy holding the electron and the nucleus together becomes increasingly negative, the radius of the orbit shrinks and more energy is needed to ionize the atom. Because a hydrogen atom with its one electron in this orbit has the lowest possible energy, this is the ground state the most stable arrangement of electrons for an element or a compound , the most stable arrangement for a hydrogen atom. Any arrangement of electrons that is higher in energy than the ground state.
Except for the negative sign, this is the same equation that Rydberg obtained experimentally. Because a sample of hydrogen contains a large number of atoms, the intensity of the various lines in a line spectrum depends on the number of atoms in each excited state. In contemporary applications, electron transitions are used in timekeeping that needs to be exact.
Telecommunications systems, such as cell phones, depend on timing signals that are accurate to within a millionth of a second per day, as are the devices that control the US power grid. Global positioning system GPS signals must be accurate to within a billionth of a second per day, which is equivalent to gaining or losing no more than one second in 1,, years. Quantifying time requires finding an event with an interval that repeats on a regular basis.
To achieve the accuracy required for modern purposes, physicists have turned to the atom. The current standard used to calibrate clocks is the cesium atom. Supercooled cesium atoms are placed in a vacuum chamber and bombarded with microwaves whose frequencies are carefully controlled. When the frequency is exactly right, the atoms absorb enough energy to undergo an electronic transition to a higher-energy state.
Decay to a lower-energy state emits radiation. In , the second was defined as the duration of 9,,, oscillations of the resonant frequency of a cesium atom, called the cesium clock. Research is currently under way to develop the next generation of atomic clocks that promise to be even more accurate.
Such devices would allow scientists to monitor vanishingly faint electromagnetic signals produced by nerve pathways in the brain and geologists to measure variations in gravitational fields, which cause fluctuations in time, that would aid in the discovery of oil or minerals. Calculate the wavelength of the lowest-energy line in the Lyman series to three significant figures.
If you look closely at the curve you will notice that the object emits some radiation at every wavelength including in the ultraviolet and infrared wavebands. You should also notice that the amount of energy emitted is not the same for all wavelengths and that in this case, the peak wavelength falls within the region of visible light. Now what happens if the temperature of the black body source is different?
The plot below shows Planck curves for an object at four different temperatures from 6, K to 4, K. How do the curves compare? Two key points should be apparent. Firstly, a hotter object emits more energy at every wavelength than a cooler one. Secondly, the hotter the object, the shorter the wavelength of the peak of the curve. The 6, K object clearly peaks in the visible part of the spectrum whereas the peak of the 4, K object borders the visible and the infrared regions.
As already mentioned, stars approximate black body objects and can vary in their effective temperatures from around 2, K to about 30, K. If you tried to plot the intensity of two stars with these extremes on a plot like the one above it would be extremely difficult to show them on the same linear scale. This is shown below for six different temperatures. You can see clearly from the plot that a 10, K star would have its peak wavelength in the ultraviolet part of the em spectrum whilst a 3, K star would emit most of its radiation in the infrared part.
Not only does the shape of the curve determine the relative intensity of the different components of the continuous spectrum produced by the star, it also determines the colour of the star. A 10, K star appears blue-white whilst a 3, K star appears red. Line spectra appear in two forms, absorption spectra, showing dark lines on a bright background, and emission spectra with bright lines on a dark or black background. These two types are in fact related and arise due to quantum mechanical interactions between electrons orbiting atoms and photons of light.
Photons of light each have a specific frequency. If we separate the incoming light from a celestial source using a prism, we will often see a spectrum of colours crossed with discrete lines. Note that spectral lines can also occur in other regions of the electromagnetic spectrum , although we can no longer use a prism to help identify them.
Emission lines are seen as coloured lines on a black background. Absorption lines are seen as black lines on a coloured background. Hydrogen Atom. Emission and absorption lines are also seen when oppositely charged ions recombine to an electrically neutral state.
The thus formed neutral atom is highly excited, with electrons transitioning between states, emitting and absorbing photons. The resulting emission and absorp-tion lines are called recombination lines. Some recombination lines occur at relatively low frequencies, well within the radio range, specifically those of carbon ions. Molecules, as well as atoms, in their gas phase also absorb characteristic narrow frequency bands of radiation passed through them. In the microwave and long wavelength infrared portions of the spectrum, these lines are due to quantized rotational motion of the molecule.
The precise fre-quencies of these absorption lines can be used to determine molecular species. This method is valuable for detecting molecules in our atmosphere, in the atmospheres of other planets, and in the interstellar medium.
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