Question

Absorption of a 2.1657 x 10³ nm photon raises an electron in hydrogen from n=4 to which quantum number, n?

a) n = 1
b) n = 2
c) n = 3
d) n = 5
e) n = 6

Answer 1

The absorption of a 2.1657 x 10^3 nm photon by a hydrogen atom results in an electron transition from n=4 to a higher energy level, which can be calculated using the known energy levels of hydrogen.

Step-by-step explanation:

The student is asking about the electron transition in a hydrogen atom after absorption of a photon with a specific wavelength in the context of quantum mechanics, which is a topic in physics. When a hydrogen atom absorbs a photon, the electron moves from a lower energy level (n=4 in this case) to a higher energy level. The energy difference between these levels corresponds to the energy of the absorbed photon.

The formula for the energy levels of a hydrogen atom is given by:

En = -13.6 eV / n2 where n is the principal quantum number. The energy of the fifth excited state (n=6) provided in the prompt is 0.378 eV, indicating that the absorbed 93.7 nm photon has raised an electron to the n=6 state.

Using the principles demonstrated, we can deduce that the absorption of a 2.1657 x 103 nm photon would also result in an electron transition to a higher, quantized energy state in the hydrogen atom, following similar calculations and understanding of quantum energy levels.