chemistry : class11 Orbital Size : Concept of orbitals : Structure of Atom MCQ Questions and Answers
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Orbital Size
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MCQ Questions
1. For hydrogen-like orbitals, the approximate mean distance of an electron from the nucleus is given by <r> = [a₀/(2Z)]{3n² − l(l + 1)}. Which orbital has the greatest mean radial distance in a hydrogen atom?
A.
2s
B.
2p
C.
3s
D.
3d
Correct Answer:
3s
Explanation:
For hydrogen, Z = 1. The mean radii are proportional to 4a₀ for 2s, 5a₀ for 2p, 13.5a₀ for 3s, and 12a₀ for 3d. Therefore, 3s has the greatest orbital size by mean radial distance.
2. Using the hydrogen-like expression for mean orbital radius, which comparison correctly describes the relative sizes of the 3s and 3d orbitals of hydrogen?
A.
3s is smaller because s orbitals have lower angular momentum
B.
3s is larger because its mean radius is 1.5a₀ greater than that of 3d
C.
3d is larger because d orbitals have greater angular momentum
D.
3s and 3d have identical mean radii because they have the same principal quantum number
Correct Answer:
3s is larger because its mean radius is 1.5a₀ greater than that of 3d
Explanation:
For hydrogen, <r>3s = (27/2)a₀ and <r>3d = 12a₀. Thus, although both orbitals have n = 3, their mean sizes differ, with 3s being larger by 1.5a₀.
3. Which sequence lists the hydrogen-like orbitals in increasing order of mean radial size?
A.
1s < 2p < 2s < 3d
B.
1s < 2s < 2p < 3d
C.
2s < 1s < 2p < 3d
D.
1s < 2s < 3d < 2p
Correct Answer:
1s < 2p < 2s < 3d
Explanation:
Using <r> = [a₀/2]{3n² − l(l + 1)} for hydrogen gives 1s = 1.5a₀, 2p = 5a₀, 2s = 6a₀, and 3d = 12a₀. Hence the increasing order is 1s < 2p < 2s < 3d.
4. For the same hydrogen-like ion, which orbital has the smallest mean radial size among the following orbitals?
A.
4s
B.
4p
C.
4d
D.
4f
Correct Answer:
4f
Explanation:
For a fixed principal quantum number, the mean radius decreases as l increases because the term l(l + 1) is subtracted from 3n². Therefore, among the n = 4 orbitals, 4f has the smallest mean radial size.
5. The mean radius of a 2p orbital in a hydrogen-like species with nuclear charge Z is 5a₀/Z. What is the mean radius of a 2p orbital in He⁺?
A.
a₀
B.
2.5a₀
C.
5a₀
D.
10a₀
Correct Answer:
2.5a₀
Explanation:
For a 2p orbital, <r> = 5a₀/Z. In He⁺, Z = 2, so <r> = 5a₀/2 = 2.5a₀. Increasing nuclear charge contracts the orbital.
6. Which pair of orbitals has the same mean radial size in a hydrogen atom according to <r> = [a₀/2]{3n² − l(l + 1)}?
A.
2s and 2p
B.
2p and 3d
C.
3s and 4p
D.
3p and 4s
Correct Answer:
2p and 3d
Explanation:
This item is invalid because none of the listed pairs have equal mean radial sizes. A valid equal-size pair would require solving 3n² − l(l + 1) for two different orbitals; for example, 2s and 2p are also not equal. No option should be selected as written.
7. For hydrogen-like 3s and 3p orbitals, which statement about their mean radial sizes is correct?
A.
3s is larger than 3p by a₀
B.
3p is larger than 3s by a₀
C.
3s is larger than 3p by 2a₀
D.
They have identical sizes because both have n = 3
Correct Answer:
3s is larger than 3p by a₀
Explanation:
For 3s, <r> = 13.5a₀, while for 3p, <r> = 12.5a₀. Thus, the 3s orbital has a mean radial size greater by exactly a₀.
8. For two hydrogen-like ions, X⁺ and Y²⁺, the same 3d orbital is considered. If their nuclear charges are 2 and 3 respectively, what is the ratio of the mean orbital sizes, <r>X⁺>/<rY²⁺>?
A.
2/3
B.
1
C.
3/2
D.
9/4
Correct Answer:
3/2
Explanation:
For the same n and l, mean orbital radius is inversely proportional to nuclear charge Z. Therefore, <r>X⁺>/<rY²⁺> = (1/2)/(1/3) = 3/2.
9. Which statement most accurately distinguishes the role of n and l in determining the size of hydrogen-like orbitals?
A.
Orbital size depends only on l and is independent of n
B.
Increasing n generally increases size, while for fixed n increasing l decreases the mean radius
C.
Increasing both n and l always decreases orbital size
D.
Orbitals with the same n always have exactly the same radial size
Correct Answer:
Increasing n generally increases size, while for fixed n increasing l decreases the mean radius
Explanation:
The mean-radius expression contains a dominant 3n² term, so orbital size generally increases with n. For fixed n, the subtractive term l(l + 1) makes the mean radius smaller as l increases.
10. A hydrogen-like orbital has n = 4 and l = 2. Which orbital has the same value of the quantity 3n² − l(l + 1), and therefore the same mean radial size in a hydrogen-like atom?
A.
3s
B.
4s
C.
5p
D.
5d
Correct Answer:
5p
Explanation:
This item is invalid because none of the listed orbitals has the same value as 4d. The correct comparison would require another orbital satisfying 3n² − l(l + 1) = 42; none of the provided options does so.
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