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1. Which of the following is the correct order of increasing orbital energy?
a) 2s 2p, 1s, 3s 3p, 3d, 4s, 4p
b) 1s, 2s 2p, 3s 3p, 4s, 3d, 4p
c) 1s, 3s 3p, 3d, 4p, 4s, 2s 2p
d) 1s, 2s 3p, 3s 2p, 3d, 4s, 4p
✅ Correct Answer: (b) 1s, 2s 2p, 3s 3p, 4s, 3d, 4p
๐๐ Short Reason
By the (n + l) rule: orbitals with lower n+l fill first; if equal, lower n comes first. So the sequence is: 1s → 2s,2p → 3s,3p → 4s → 3d → 4p.
๐๐ง Reasoning (Aufbau Principle + (n + l) Rule)
๐The order of orbital energies is determined by the Aufbau principle and the (n + l) rule. According to this rule, orbitals with lower n+l values fill first; if two orbitals have the same n+l, the one with lower n is lower in energy. Applying this:
๐ฅ1s (n+l=1) is the lowest.
๐ฅ2s (2), 2p (3) come next.
๐ฅ3s (3), 3p (4) follow.
๐ฅ4s (4) is slightly lower than 3d (5).
๐ฅFinally, 4p (5) is higher than 3d because of its larger n.
๐Applying this:
๐ฅ1s → n=1,l=0→n+l=1 → lowest energy.
๐ฅ2s (n=2,l=0 → 2) and 2p (n=2,l=1 → 3) → next.
๐ฅ3s (n=3,l=0 → 3) and 3p (n=3,l=1 → 4) → next.
๐ฅ4s (n=4,l=0 → 4) → comes before 3d.
๐ฅ3d (n=3,l=2 → 5) → higher than 4s.
๐ฅ4p (n=4,l=1 → 5) → similar n+l but higher n, so after 3d.
๐ ๐ Thus, the correct increasing energy sequence is 1s → 2s,2p → 3s,3p → 4s → 3d → 4p (1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p), which matches option (b).
๐๐ Short Reason
By the (n + l) rule: orbitals with lower n+l fill first; if equal, lower n comes first. So the sequence is: 1s → 2s,2p → 3s,3p → 4s → 3d → 4p.
๐๐ง Reasoning (Aufbau Principle + (n + l) Rule)
๐The order of orbital energies is determined by the Aufbau principle and the (n + l) rule. According to this rule, orbitals with lower n+l values fill first; if two orbitals have the same n+l, the one with lower n is lower in energy. Applying this:
๐ฅ1s (n+l=1) is the lowest.
๐ฅ2s (2), 2p (3) come next.
๐ฅ3s (3), 3p (4) follow.
๐ฅ4s (4) is slightly lower than 3d (5).
๐ฅFinally, 4p (5) is higher than 3d because of its larger n.
๐Applying this:
๐ฅ1s → n=1,l=0→n+l=1 → lowest energy.
๐ฅ2s (n=2,l=0 → 2) and 2p (n=2,l=1 → 3) → next.
๐ฅ3s (n=3,l=0 → 3) and 3p (n=3,l=1 → 4) → next.
๐ฅ4s (n=4,l=0 → 4) → comes before 3d.
๐ฅ3d (n=3,l=2 → 5) → higher than 4s.
๐ฅ4p (n=4,l=1 → 5) → similar n+l but higher n, so after 3d.
๐ ๐ Thus, the correct increasing energy sequence is 1s → 2s,2p → 3s,3p → 4s → 3d → 4p (1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p), which matches option (b).
2. Which of the following pairs of gases have exactly double the rate of diffusion as each other?
a) N₂ and SO₃
b) He and CH₄
c) CO and SO₂
d) O₃ and F₂
✅ Correct Answer: (b) He and CH₄
๐๐ Short Reason
By Graham’s Law, the diffusion rate ratio depends on the square root of molar mass ratio. Only He (4 g/mol) and CH₄ (16 g/mol) give a perfect square root ratio of 2, meaning helium diffuses exactly twice as fast as methane.
๐ ๐ Detailed Reasoning
According to Graham’s Law, the rate of diffusion of a gas is inversely proportional to the square root of its molar mass i.e. r ∝ 1/√M
So, for two gases A and B: rแด/rะฒ =√Mะฒ/√Mแด
๐ Step by Step Check
๐ (a) N₂ (28 g/mol) and SO₃ (80 g/mol): rN₂/rSO₃ = √80/√28 ≈1.69 → Not exactly 2. ❌
๐ (b) He (4 g/mol) and CH₄ (16 g/mol): rสโ/rัส₄ = √16/√4 = 4 = 2 →✅ Exactly double.
๐ (c) CO (28 g/mol) and SO₂(64 g/mol): rCO/rSO2 = √64/√28 ≈ 1.51 → Not exactly 2. ❌
๐ (d) O₃ (48 g/mol) and F₂ (38 g/mol): rF₂/rแฝน₃ = √48/√38 ≈ 1.12 → Not exactly 2. ❌
๐๐ Short Reason
By Graham’s Law, the diffusion rate ratio depends on the square root of molar mass ratio. Only He (4 g/mol) and CH₄ (16 g/mol) give a perfect square root ratio of 2, meaning helium diffuses exactly twice as fast as methane.
๐ ๐ Detailed Reasoning
According to Graham’s Law, the rate of diffusion of a gas is inversely proportional to the square root of its molar mass i.e. r ∝ 1/√M
So, for two gases A and B: rแด/rะฒ =√Mะฒ/√Mแด
๐ Step by Step Check
๐ (a) N₂ (28 g/mol) and SO₃ (80 g/mol): rN₂/rSO₃ = √80/√28 ≈1.69 → Not exactly 2. ❌
๐ (b) He (4 g/mol) and CH₄ (16 g/mol): rสโ/rัส₄ = √16/√4 = 4 = 2 →✅ Exactly double.
๐ (c) CO (28 g/mol) and SO₂(64 g/mol): rCO/rSO2 = √64/√28 ≈ 1.51 → Not exactly 2. ❌
๐ (d) O₃ (48 g/mol) and F₂ (38 g/mol): rF₂/rแฝน₃ = √48/√38 ≈ 1.12 → Not exactly 2. ❌
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