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Chapter 38: Problem 32

Electrons with the same value of quantum number \(n\) are said to occupy the same electron shell \(K, L, M, N,\) etc. Calculate the maximum allowed number of electrons for the a) \(K\) shell, b) \(L\) shell, and c) \(M\) shell.

Short Answer

Expert verified
Answer: The maximum allowed number of electrons for the K, L, and M electron shells are 2, 8, and 18 respectively.

Step by step solution

01

Understand the formula

We are using the formula to calculate the maximum allowed number of electrons in a given shell. The formula is: \(max \, electrons \, = 2n^2\) where \(n\) represents the principal quantum number.
02

Calculate for the K shell

For the \(K\) shell, the principal quantum number \(n = 1\). Using the formula, we have: \(max \, electrons \, (K) = 2(1^2) = 2(1) = 2\). So, the maximum allowed number of electrons for the \(K\) shell is 2.
03

Calculate for the L shell

For the \(L\) shell, the principal quantum number \(n = 2\). Using the formula, we have: \(max \, electrons \, (L) = 2(2^2) = 2(4) = 8\). So, the maximum allowed number of electrons for the \(L\) shell is 8.
04

Calculate for the M shell

For the \(M\) shell, the principal quantum number \(n = 3\). Using the formula, we have: \(max \, electrons \, (M) = 2(3^2) = 2(9) = 18\). So, the maximum allowed number of electrons for the \(M\) shell is 18. In summary, the maximum allowed number of electrons for the: a) \(K\) shell is 2, b) \(L\) shell is 8, and c) \(M\) shell is 18.

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