Which sub-shell has highest energy?

Explanation

The correct option is a) n=5, ℓ=3, m=+1. The energy of an electron in an atom depends on its principal quantum number (n), azimuthal quantum number (ℓ), and magnetic quantum number (m). The general trend is that as the principal quantum number increases, the energy of the subshell also increases. Additionally, within a given principal quantum number, the energy increases as the azimuthal quantum number increases. Let's analyze the other options to understand why they are incorrect: b) n=5, ℓ=2, m=+2: This subshell has a lower energy compared to option a. The azimuthal quantum number (ℓ) is lower, which indicates a lower energy level. Therefore, option b has a lower energy than option a. c) n=4, ℓ=3, m=0: This subshell has a lower energy compared to option a. The principal quantum number (n) is lower, which indicates a lower energy level. Therefore, option c has a lower energy than option a. d) n=4, ℓ=0, m=+1: This subshell has a lower energy compared to option a. The azimuthal quantum number (ℓ) is lower, which indicates a lower energy level. Therefore, option d has a lower energy than option a. In summary, option a has the highest energy among the given choices because it has the highest principal quantum number (n=5) and highest azimuthal quantum number (ℓ=3).