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The brightness of an atomic emission line is determined by the number of atoms that are excited to the upper energy level and the probability of the transition between the upper and lower energy levels.
Factors that affect the number of excited atoms include the temperature of the sample and the concentration of the element in the sample. The probability of the transition is determined by the selection rules for the transition and the strength of the electric dipole moment between the upper and lower energy levels.
In general, transitions that are allowed by the selection rules and have a strong electric dipole moment will be brighter than transitions that are forbidden by the selection rules or have a weak electric dipole moment.