When an electron makes a transition between energy levels of...

When an electron makes a transition between energy levels of an atom, there are no restrictions on the initial and final values of the principal quantum number $n .$ According to quantum mechanics, however, there is a rule that restricts the initial and final values of the orbital quantum number $\ell$. This rule is called a selection rule and states that $\Delta \ell=\pm 1 .$ In other words, when an electron makes a transition between energy levels, the value of $t$ can only increase or decrease by one. The value of $\ell$ may not remain the same nor may it increase or decrease by more than one. According to this rule, which of the following energy level transitions are allowed? (a) $2 \mathrm{s} \rightarrow 1 \mathrm{s}$ (b) $2 p \rightarrow$ Is $(c) 4 p \rightarrow 2 p$ (d) $4 \mathrm{s} \rightarrow 2 \mathrm{p}$ (e) $3 \mathrm{d} \rightarrow 3 \mathrm{s}$

When an electron makes a transition between energy levels of an atom, there are no restrictions on the initial and final values of the principal quantum number $n .$ According to quantum mechanics, however, there is a rule that restricts the initial and final values of the orbital quantum number $\ell$. This rule is called a selection rule and states that $\Delta \ell=\pm 1 .$ In other words, when an electron makes a transition between energy levels, the value of $t$ can only increase or decrease by one. The value of $\ell$ may not remain the same nor may it increase or decrease by more than one. According to this rule, which of the following energy level transitions are allowed?
(a) $2 \mathrm{s} \rightarrow 1 \mathrm{s}$
(b) $2 p \rightarrow$ Is $(c) 4 p \rightarrow 2 p$
(d) $4 \mathrm{s} \rightarrow 2 \mathrm{p}$
(e) $3 \mathrm{d} \rightarrow 3 \mathrm{s}$

Key Concepts

Quantum Transitions

Quantum transitions refer to the movement of an electron between different energy states or orbitals in an atom. This process involves the electron absorbing or emitting energy, typically in the form of photons, allowing it to jump from one quantized energy level to another. These transitions are fundamental to understanding atomic spectra and the behavior of electrons in atoms.

Principal Quantum Number

The principal quantum number, denoted as n, primarily determines the energy level or shell in which an electron resides within an atom. While it sets the overall energy scale for an electron's state, transitions between energy levels governed solely by n do not have the same restrictive selection rules as those involving angular momentum changes.

Orbital Angular Momentum Quantum Number

The orbital angular momentum quantum number, denoted as l, describes the shape of the electron's orbital and its angular momentum. This quantum number plays a critical role in defining atomic orbitals (such as s, p, d, etc.) and influences the electron’s spatial distribution. In electronic transitions, changes in l are closely inspected to determine if a transition is quantum mechanically allowed or forbidden.

Selection Rules

Selection rules are guidelines derived from quantum mechanics that dictate which electron transitions are allowed based on the conservation of angular momentum and other symmetries. A common selection rule for electric dipole transitions is that the change in the orbital quantum number must be ?l = ±1. This rule restricts the possible transitions between orbitals, ensuring that only transitions with the appropriate change in angular momentum occur.

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