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5. Using the standard selection rules for radiative decay (a) What states can an electron in 4d state decay into? (b) If we observe a transition from the n=5 to the n=2 state, what are all the allowed pairs of initial and final l

5. Using the standard selection rules for radiative decay (a) What states can an electron in 4d state decay into? (b) If we observe a transition from the n=5 to the n=2 state, what are all the allowed pairs of initial and final l

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### Topic: Radiative Decay and Selection Rules 5. **Using the Standard Selection Rules for Radiative Decay:** **(a)** What states can an electron in the 4d state decay into? **(b)** If we observe a transition from the \( n=5 \) to the \( n=2 \) state, what are all the allowed pairs of initial and final \( \ell \) (orbital quantum numbers)? ### Explanation: This segment focuses on the application of selection rules in the context of radiative decay, a key concept in quantum mechanics and atomic physics. Selection rules determine the allowed transitions between quantum states, a fundamental aspect for understanding processes like photon emission and absorption. - **For Part (a):** - Involves identifying possible final states for an electron initially in a 4d state. The determination depends on quantum numbers and the rules which allow or forbid certain transitions. - **For Part (b):** - Focuses on determining the valid pairs of initial and final orbital quantum numbers (\( \ell \)) during a transition from a high energy level (n=5) to a lower one (n=2). The selection rules dictate how \(\ell\) can change during transitions, typically by \(|\Delta \ell| = 1\). This content is aimed at students studying atomic structure in physics or chemistry, helping them understand the principles governing electron transitions in atoms.
Transcribed Image Text:### Topic: Radiative Decay and Selection Rules 5. **Using the Standard Selection Rules for Radiative Decay:** **(a)** What states can an electron in the 4d state decay into? **(b)** If we observe a transition from the \( n=5 \) to the \( n=2 \) state, what are all the allowed pairs of initial and final \( \ell \) (orbital quantum numbers)? ### Explanation: This segment focuses on the application of selection rules in the context of radiative decay, a key concept in quantum mechanics and atomic physics. Selection rules determine the allowed transitions between quantum states, a fundamental aspect for understanding processes like photon emission and absorption. - **For Part (a):** - Involves identifying possible final states for an electron initially in a 4d state. The determination depends on quantum numbers and the rules which allow or forbid certain transitions. - **For Part (b):** - Focuses on determining the valid pairs of initial and final orbital quantum numbers (\( \ell \)) during a transition from a high energy level (n=5) to a lower one (n=2). The selection rules dictate how \(\ell\) can change during transitions, typically by \(|\Delta \ell| = 1\). This content is aimed at students studying atomic structure in physics or chemistry, helping them understand the principles governing electron transitions in atoms.
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