chemistry question

Question

How many electrons in an atom could have these sets of quantum numbers?

n = 3: _____ electrons

n =5,ℓ=2: ______ electrons

𝑛=7,ℓ=2,𝑚_ℓ= -1: ______ electrons

Answer 1

n=3 indicates the 3rd energy level which contains 3s, 3p and 3d orbitals. The s can hold 2 electrons. The p can hold 6 electrons and the d can hold 10 electrons. Total = 18 electrons

n = 5, ℓ=2 indicates the 5th energy level and d orbital. The d orbital can contain 14 electrons

n = 7, ℓ=2,𝑚_ℓ= -1 indicates the 7th energy level and d orbital, but the 𝑚_ℓ= -1 tells us the orientation of the d orbital. For ℓ=2,𝑚_ℓ can be -2, -1, 0, +1, +2 so if it is -1, there are 2 electrons that can occupy that space.