Question

In which of the following, orbitals are correctly arranged in the increasing order of their energies?

• A. 4f < 5p < 5d <6s
• B. 5p < 4f < 6s < 5d
• C. 5p < 6s < 4f < 5d
• D. 5p < 5d < 4f < 6s

Hint:

Use the (n+l) rule to determine the order of filling orbitals. Lower (n+l) values indicate lower energy. If (n+l) is the same, lower n indicates lower energy.

Answer 1

The Correct Option is C

Step 1: Understand the Aufbau principle and Hund's rule. The Aufbau principle states that electrons first fill the lowest energy orbitals available. Hund's rule states that within a subshell, electrons will individually occupy each orbital before doubling up in any one orbital.
Step 2: Apply the (n+l) rule. The energy of an orbital is determined by the (n+l) rule, where n is the principal quantum number and l is the azimuthal quantum number (l = 0 for s, 1 for p, 2 for d, 3 for f).
Step 3: Determine the (n+l) values for each orbital.
5p: n = 5, l = 1, n+l = 6
6s: n = 6, l = 0, n+l = 6
4f: n = 4, l = 3, n+l = 7
5d: n = 5, l = 2, n+l = 7
When orbitals have the same (n+l) value, the orbital with the lower n value has lower energy. Therefore, 5p<6s and 4f<5d.
Step 4: Determine the correct order.
5p and 6s have lower (n+l) values than 4f and 5d, so they must come first. Comparing 5p and 6s, 5p has a lower n value, so 5p < 6s. Comparing 4f and 5d, 4f has a lower n value, so 4f< 5d. Combining these, the correct order is 5p <6s< 4f < 5d. Final Answer: \[ \boxed{5p<6s<4f<5d} \]