Final answer:
When a hydrogen atom's electron moves from n=2 to n=3, it absorbs energy; the corresponding photon frequency can be calculated using the energy difference and Planck's constant. Photons in the visible range of energy are emitted when electrons fall to lower energy levels, explaining why heated hydrogen emits colored light.
Step-by-step explanation:
Energy Transition in a Hydrogen Atom
When an electron in a hydrogen atom transitions from the n=2 to n=3 energy level, energy is absorbed as the electron is moving to a higher energy state. The energy levels of a hydrogen atom are quantized and the difference in energy between these levels corresponds to the energy of a photon that must be absorbed for the transition to occur. In the question, the energy for n=2 is given as -3.4 eV and for n=3 it's -1.5 eV, hence the energy difference (ΔE) is 1.9 eV (|-1.5 eV| - |-3.4 eV|=ΔE). To find the frequency (ν) of the photon that corresponds to this energy, we use the formula E = hν, where E is the energy of the photon, h is Planck's constant (h = 6.626 x 10^-34 J s), and ν is the frequency. Converting the energy from electron volts to joules (1 eV = 1.602 x 10^-19 J), we can calculate the frequency of the photon.
For the transition from n=2 to n=1, energy is emitted as the electron moves to a lower energy state. Using the same method, we can determine the frequency of the emitted photon. To determine if a photon is in the visible range, we need to compare its energy with the known range of photon energies for visible light, which is from 1.63 to 3.26 eV. If the energy of the photon falls within this range, it is visible light.
Regarding the sample of hydrogen gas glowing with a pale pink color, this behavior is best explained by option 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. This is because discrete energy levels within the hydrogen atoms allow for the emission of photons with specific energies, corresponding to the difference in energy between the levels, which are perceived as different colors when combined.