For each of the questions, four choices have been provided. Select the correct alternative. Among the following, the orbital that has the lowest energy is (a) \(5 \mathrm{f}\) (b) \(4 \mathrm{f}\) (c) \(6 \mathrm{~s}\) (d) \(6 \mathrm{p}\)

Short Answer

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Answer: (c) 6s

Step by step solution

01

Common Understanding of Quantum Numbers

The principal quantum number (n) denotes the energy level and the distance from the nucleus (higher n, higher energy levels). The azimuthal quantum number (l) represents the shape of the orbital, where, for example, l=0 is designated as "s," l=1 as "p," and l=2 as "d."
02

Assign Quantum Numbers to the Given Options

Assign the principal quantum number (n) and azimuthal quantum number (l) for each option: (a) 5f: n=5, l=3 (b) 4f: n=4, l=3 (c) 6s: n=6, l=0 (d) 6p: n=6, l=1
03

Calculate the Sum n+l for Each Option

Determine the sum n+l for each option: (a) 5f: 5+3=8 (b) 4f: 4+3=7 (c) 6s: 6+0=6 (d) 6p: 6+1=7
04

Determine the Orbital with the Lowest Energy

The orbital with the lowest energy corresponds to the option with the smallest sum n+l. In this case, it is option (c) 6s with n+l=6. Therefore, among the given orbital options, the orbital with the lowest energy is (c) 6s.

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