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For example, radiation emitted from a distant rotating body, such as a star, will be broadened due to the line-of-sight variations in velocity on opposite sides of the star (this effect usually referred to as rotational broadening). The greater the rate of rotation, the broader the line. Another example is an imploding plasma shell in a Z-pinch.
An extreme example of this effect is the influence of hydrogen bonding on the spectra of protic liquids. Observed spectral line shape and line width are also affected by instrumental factors. The observed line shape is a convolution of the intrinsic line shape with the instrument transfer function .
The spectrum appears in a series of lines called the line spectrum. This line spectrum is called an atomic spectrum when it originates from an atom in elemental form. Each element has a different atomic spectrum. The production of line spectra by the atoms of an element indicate that an atom can radiate only a certain amount of energy.
When any integer higher than 2 was squared and then divided by itself squared minus 4, then that number multiplied by 364.506 82 nm (see equation below) gave the wavelength of another line in the hydrogen spectrum. By this formula, he was able to show that some measurements of lines made in his time by spectroscopy were slightly inaccurate, and ...
The equivalent width of a spectral line is a measure of the area of the line on a plot of intensity versus wavelength in relation to underlying continuum level. It is found by forming a rectangle with a height equal to that of continuum emission, and finding the width such that the area of the rectangle is equal to the area in the spectral line.
The four visible hydrogen emission spectrum lines in the Balmer series. H-alpha is the red line at the right. The Balmer series includes the lines due to transitions from an outer orbit n > 2 to the orbit n' = 2. Named after Johann Balmer, who discovered the Balmer formula, an empirical equation to predict
As a result, each line in a spectrum has its own set of associated coefficients. When the atoms and the radiation field are in equilibrium, the radiance will be given by Planck's law and, by the principle of detailed balance, the sum of these rates must be zero: 0 = A 21 n 2 + B 21 n 2 4 π c B ν ( T ) − B 12 n 1 4 π c B ν ( T ...
Line spectral pairs have several interesting and useful properties. When the roots of P(z) and Q(z) are interleaved, stability of the filter is ensured if and only if the roots are monotonically increasing. Moreover, the closer two roots are, the more resonant the filter is at the corresponding frequency.