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Choose the correct option regarding ener...

Choose the correct option regarding energy of empty orbitals.
`{:(,n,l,m,s),((I),4,0,0,+1/2),((II),3,2,0,-1/2),((III),3,1,1,+1/2),((IV),3,0,0,-1/2):}`

A

`I gt IV`

B

`II gt I`

C

`II gt III`

D

`I = III`

Text Solution

AI Generated Solution

The correct Answer is:
To solve the question regarding the energy of empty orbitals, we will analyze the given orbitals based on their quantum numbers and apply the n + l rule. Here’s a step-by-step breakdown of the solution: ### Step 1: Identify the Orbitals We have four sets of quantum numbers (n, l, m, s): 1. (I) (4, 0, 0, +1/2) - This corresponds to the 4s orbital. 2. (II) (3, 2, 0, -1/2) - This corresponds to the 3d orbital. 3. (III) (3, 1, 1, +1/2) - This corresponds to the 3p orbital. 4. (IV) (3, 0, 0, -1/2) - This corresponds to the 3s orbital. ### Step 2: Calculate n + l Values Next, we calculate the n + l values for each orbital: - For (I) 4s: n + l = 4 + 0 = 4 - For (II) 3d: n + l = 3 + 2 = 5 - For (III) 3p: n + l = 3 + 1 = 4 - For (IV) 3s: n + l = 3 + 0 = 3 ### Step 3: Determine Energy Order Using the n + l rule, we can determine the order of energy levels: - The higher the n + l value, the higher the energy of the orbital. - If two orbitals have the same n + l value, the one with the higher n value has higher energy. From our calculations: - 3s (n + l = 3) has the lowest energy. - 4s (n + l = 4) and 3p (n + l = 4) have the same n + l value, but since 4s has a higher n value than 3p, 4s is higher in energy than 3p. - 3d (n + l = 5) has the highest energy. ### Step 4: Final Energy Order Based on the analysis, the order of increasing energy is: 1. 3s (lowest energy) 2. 4s 3. 3p 4. 3d (highest energy) ### Conclusion Thus, the correct order of increasing energy of the empty orbitals is: 3s < 4s < 3p < 3d.
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