Question 13 of 48intermediate🔧 ApplyShort Answer2 marks

On the basis of quantum numbers, justify that the sixth period of the periodic table should have 32 elements.

Correct Answer

For the sixth period, the highest principal quantum number is n=6n=6. Successive electrons enter the 6s, 4f, 5d, and 6p orbitals in that order.

The total number of atomic orbitals available in this energy level is 16 (one 6s, seven 4f, five 5d, and three 6p orbitals). Since the number of elements in a period is twice the number of atomic orbitals available, the maximum number of electrons that can be accommodated is 2×16=322 \times 16 = 32.

Therefore, the sixth period contains 32 elements, which includes the 4f-inner transition series known as the lanthanoids.

Exercise: EXERCISES | Q: 3.4 | (Page 23)
For More Understanding

Explanation

The context explains that the sixth period corresponds to n=6, where electrons fill the 6s, 4f, 5d, and 6p orbitals. Counting these orbitals gives 1 + 7 + 5 + 3 = 16 orbitals. Since each orbital holds 2 electrons, 16 orbitals accommodate 32 electrons, justifying 32 elements in the period.

Solution Steps

  1. Step 1: Identify the principal quantum number for the sixth period (n=6n=6) and the orbitals filled: 6s, 4f, 5d, and 6p.

  2. Step 2: Calculate the total number of available orbitals: 1 (6s) + 7 (4f) + 5 (5d) + 3 (6p) = 16 orbitals.

  3. Step 3: Multiply the total orbitals by 2 (since each orbital holds 2 electrons) to get the maximum number of elements: 2×16=322 \times 16 = 32 elements.

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