Final answer:
The frequency of light emitted during an electron transition in a hydrogen atom is calculated by finding the energy difference between the initial and final energy levels and then dividing by Planck's constant. The distinct colors seen when hydrogen gas is heated are due to these electron transitions.
Step-by-step explanation:
The frequency of the light emitted by a hydrogen atom when an electron transitions between different energy levels can be calculated using the formula for the energy of a photon, which is \(E=hf\), where \(E\) is the energy, \(h\) is Planck's constant, and \(f\) is the frequency. The energy difference \(\Delta E\) between two levels for a hydrogen atom is given by \(\Delta E = E_{final} - E_{initial}\). To find the frequency, rearrange the formula to \(f = \Delta E / h\).
For example, for an electron transitioning from \(n=4\) to \(n=3\), we would first calculate the energy difference between these levels and then divide by Planck's constant to find the frequency. The same steps follow for each of the other transitions listed.
To answer the conceptual question from the provided information, the emission of light by a heated hydrogen gas is best explained by selection b: As the gas heats up, the electrons within the hydrogen atoms are excited to high energy levels. As the electrons transition to lower energies, they emit light of specific colors.