A 5d electron emits a photon, what are the possible quantum n,l, quantum numbers of the final s tate electron? What would the quantum num bers be a fter a photon with the smallest allowed (non-zero) energy is emitted?
Sketch the energy level diagram for atomic orbitals from 1s to 2s etc up to 5d. Then delta l can be +/-1 ONLY. Is 4f the next energy level down. If so then delta l (where l is 2 with a 5d) can go to 4f where the delta l is +1 or from 5d to 4p where delta l is -1. The series then could be 5d to 4p, 5d to 3p, 5d to 2p. The other selection rule is that ml can be 0,+/-1. This should get you started with the hard part. Then fill in the other quantum numbers given the transitions I've shown. It appears to me that the 5d to 4f is the transition with the smallest energy emitted.
To determine the possible quantum numbers of the final state electron after a 5d electron emits a photon, we need to understand the rules governing the emission of photons and the behavior of electrons in an atom.
1. Energies of Photons: The energy of a photon emitted or absorbed is given by the equation E = hf, where E represents the energy, h is Planck's constant (approximately 6.626 x 10^-34 Joule-seconds), and f is the frequency of the photon.
2. Electron Transitions: When an electron transitions from a higher energy level to a lower energy level, it emits a photon with an energy equivalent to the energy difference between the two levels. Each energy level in an atom is characterized by a principal quantum number (n) and an orbital angular momentum quantum number (l).
Given that a 5d electron emits a photon, it means that the transition occurs from the 5d orbital to another orbital at a lower energy level.
Let's determine the possible quantum numbers of the final state electron:
1. Quantum Number n: The principal quantum number n refers to the energy level of the electron. The energy levels are quantized, and in the case of a hydrogen-like atom (with one electron), the possible values of n are positive integers starting from 1. Therefore, since the 5d electron emits a photon, the final state electron could occupy energy levels with n less than 5.
2. Quantum Number l: The orbital angular momentum quantum number l indicates the shape of the orbital. It can have values ranging from 0 to n-1 for a given value of n. In the case of a 5d orbital, the possible values of l would be 0, 1, 2, 3, or 4.
Therefore, the possible quantum numbers of the final state electron after a 5d electron emits a photon would depend on the specific final energy level to which it transitions. Without additional information about the final energy level, we cannot determine the exact values of n and l.
Regarding the quantum numbers after emitting a photon with the smallest nonzero energy:
Since the photon energy is smallest nonzero, it indicates that the transition occurs to the nearest lower energy level. In this case, the final state electron would transition to the 5s orbital, as it has the nearest lower energy to the 5d orbital.
For the 5s orbital, the quantum numbers would be:
1. Quantum Number n: Since the electron transitions from the 5d to the 5s orbital, the value of n remains the same, which is 5.
2. Quantum Number l: The s orbital has a shape with l = 0.
Therefore, the quantum numbers of the final state electron after emitting a photon with the smallest allowed (non-zero) energy would be n = 5 and l = 0.