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Chapter 36: Problem 26

An infinite square well contains nine electrons. Find the energy of the highest-energy electron in terms of the ground-state energy \(\vec{E}_{1}\)

Short Answer

Expert verified
The energy of the highest-energy electron, in this case the ninth electron, is 16 times the ground-state energy, i.e., \(E_9 = 16E_1\).

Step by step solution

01

Determine the Occupation of Energy Levels

As the Pauli Exclusion Principle states, each energy level can be occupied by two electrons with opposite spins. Therefore, the first level will be occupied by 2 electrons, the second level by another 2 electrons, the third level by 2 more electrons and the fourth level by the last 3 remaining electrons. Thus, the ninth electron will be in the fourth energy level.
02

Calculate the Energy of the Ninth Electron

Given the formula \(E_n = n^2E_1\) for each energy level, we substitute \(n = 4\) because the ninth electron is in the fourth energy level. Therefore, the energy of the ninth electron in terms of the ground state energy is \(E_9 = 4^2E_1 = 16E_1\).

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Most popular questions from this chapter

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