Given below are the quantum numbers for 4 electrons.
A. n=3, l=2, ml=1,ms=+\(\frac{1}{2}\)
B. n=4, l=1, ml=0,ms=+\(\frac{1}{2}\)
C. n=4, l=2, ml=–2,ms=–\(\frac{1}{2}\)
D. n=3, l=1, ml=–1,ms=+\(\frac{1}{2}\)
The correct order of increasing energy is
Given below are the quantum numbers for 4 electrons.
A. n=3, l=2, ml=1,ms=+\(\frac{1}{2}\)
B. n=4, l=1, ml=0,ms=+\(\frac{1}{2}\)
C. n=4, l=2, ml=–2,ms=–\(\frac{1}{2}\)
D. n=3, l=1, ml=–1,ms=+\(\frac{1}{2}\)
The correct order of increasing energy is
- D < B < A < C
- D < A < B < C
- D < A < B < C
- B < D < A < C
The Correct Option is B
Approach Solution - 1
To find the correct order of increasing energy for the given electrons according to their quantum numbers, we must understand how the energy levels are determined by quantum numbers.
The energy of an electron in an atom mainly depends on its principal quantum number (n) and azimuthal quantum number (l). Higher values of n and l mean higher energy levels. The following rule is often applied:
- Electrons are filled in increasing order of (n + l) value.
- If two orbitals have the same (n + l) value, the orbital with the lower n value is filled first.
Let's determine the (n + l) values for the given electrons:
- A. n = 3, l = 2: (n + l) = 3 + 2 = 5
- B. n = 4, l = 1: (n + l) = 4 + 1 = 5
- C. n = 4, l = 2: (n + l) = 4 + 2 = 6
- D. n = 3, l = 1: (n + l) = 3 + 1 = 4
Based on these values, the order of increasing energy is determined by sorting according to (n + l), followed by n if there's a tie:
- D: (n + l) = 4
- A: (n + l) = 5, n = 3
- B: (n + l) = 5, n = 4
- C: (n + l) = 6
Therefore, the correct order of increasing energy levels is D < A < B < C.
Approach Solution -2
Energy of the sub-shell is given by, (n + l) rule.
| For | (n + l) |
|---|---|
| A | 5 |
| B | 5 |
| C | 6 |
| D | 4 |
Hence, the correct order of increasing energy is D < A < B < C
The correct option is (B): D < A < B < C.
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Concepts Used:
Electronic Configuration of Atoms
Electronic configuration, also called electronic structure, the arrangement of electrons in energy levels around an atomic nucleus. According to the older shell atomic model, electrons occupy several levels from the first shell nearest the nucleus, K, through the seventh shell, Q, farthest from the nucleus. Electrons have to be filled in the s, p, d, f in accordance with the following rule.For example, the electron configuration of sodium is 1s22s22p63s1.
Writing Electron Configurations:
Maximum number of electrons that can be accommodated in a shell is based on the principal quantum number (n). It is represented by the formula 2n2, where ‘n’ is the shell number.
Filling of Atomic Orbitals:
1. Aufbau’s principle: The filling of electrons should take place in accordance with the ascending order of energy of orbitals:
- Lower energy orbital should be filled first and higher energy levels.
- The energy of orbital α(p + l) value it two orbitals have same (n + l) value, E α n
- Ascending order of energy 1s, 2s, 2p, 3s, 3p, 4s, 3d, . . .
2. Pauli’s exclusion principle: No two electrons can have all the four quantum numbers to be the same or if two electrons have to be placed in an energy state they should be placed with opposite spies.
3. Hund’s rule of maximum multiplicity: In the case of filling degenerate (same energy) orbitals, all the degenerate orbitals have to be singly filled first and then only pairing has to happen.