chemistry : class11 Probability Density : Concept of orbitals : Structure of Atom MCQ Questions and Answers
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Probability Density
MCQ questions and answers.
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MCQ Questions
1. For a normalized orbital wave function ψ, the quantity |ψ|² dτ represents:
A.
The probability of finding the electron in the volume element dτ
B.
The energy possessed by the electron in the volume element dτ
C.
The radial distance of the electron from the nucleus
D.
The probability of finding the electron at exactly one point
Correct Answer:
The probability of finding the electron in the volume element dτ
Explanation:
The square of the magnitude of the wave function, |ψ|², is the probability density. Multiplication by a small volume element dτ gives the probability of finding the electron within that volume.
2. At a node of an orbital, which statement about probability density is correct?
A.
The probability density is maximum
B.
The probability density is zero
C.
The probability density is equal to the average density
D.
The probability density becomes negative
Correct Answer:
The probability density is zero
Explanation:
At a node, the wave function ψ is zero. Since probability density is |ψ|², it is also zero at that location.
3. Two wave functions ψ and −ψ describe the same electron probability distribution because:
A.
Their energies are necessarily different
B.
Their probability densities are identical
C.
Their radial distances are opposite
D.
Their quantum numbers become interchanged
Correct Answer:
Their probability densities are identical
Explanation:
The probability density depends on the square of the magnitude of the wave function. Thus, |ψ|² = |−ψ|², even though the wave functions have opposite signs.
4. For a normalized wave function, the integral of probability density over all space is:
A.
0
B.
1
C.
Equal to the principal quantum number
D.
Equal to the orbital energy
Correct Answer:
1
Explanation:
Normalization requires that the total probability of finding the electron somewhere in space be unity. Mathematically, the integral of |ψ|² over all space equals 1.
5. Which statement correctly distinguishes probability density from probability in a finite region?
A.
Probability density is obtained by integrating probability over a region
B.
Probability in a region is obtained by integrating probability density over that region
C.
Probability density and probability always have identical numerical values
D.
Probability is independent of the volume of the region considered
Correct Answer:
Probability in a region is obtained by integrating probability density over that region
Explanation:
Probability density is a local quantity represented by |ψ|². The probability of finding the electron in a finite region is obtained by integrating |ψ|² dτ throughout that region.
6. If the probability density at a point is doubled while the volume element remains unchanged, the probability of finding the electron in that element will:
A.
Be halved
B.
Remain unchanged
C.
Double
D.
Become zero
Correct Answer:
Double
Explanation:
For a fixed small volume element, probability is approximately probability density multiplied by the volume. Therefore, doubling the density doubles the probability in that element.
7. An orbital has a nonzero wave function at a point, but the wave function is negative there. What is the implication for probability density at that point?
A.
The probability density is negative
B.
The probability density is positive
C.
The probability density is necessarily zero
D.
The electron cannot exist at that point
Correct Answer:
The probability density is positive
Explanation:
Probability density is |ψ|², so the sign of ψ does not affect it. A nonzero negative wave function still gives a positive probability density.
8. Which expression gives the probability of finding an electron within a small volume element dx dy dz at coordinates (x, y, z)?
A.
ψ dx dy dz
B.
ψ² dx dy dz
C.
|ψ|² dx dy dz
D.
1 divided by ψ dx dy dz
Correct Answer:
|ψ|² dx dy dz
Explanation:
The volume element in Cartesian coordinates is dτ = dx dy dz. The probability of finding the electron in it is |ψ(x,y,z)|² dτ.
9. A region has a high probability density but an extremely small volume. Compared with a larger region having a lower probability density, its total probability of containing the electron:
A.
Must always be greater
B.
Must always be smaller
C.
Depends on the integral of density over the respective regions
D.
Is always exactly equal
Correct Answer:
Depends on the integral of density over the respective regions
Explanation:
Total probability depends on both the magnitude of probability density and the volume over which it is integrated. A high density does not alone guarantee a greater total probability.
10. If an orbital wave function is multiplied everywhere by a constant factor k and remains normalized only after renormalization, how does its unnormalized probability density change before renormalization?
A.
It changes by a factor k
B.
It changes by a factor k² in magnitude
C.
It changes by a factor 1 divided by k
D.
It does not change for any value of k
Correct Answer:
It changes by a factor k² in magnitude
Explanation:
For a transformed wave function kψ, the probability density is |kψ|² = |k|²|ψ|². For a real constant k, this corresponds to a factor k² before normalization is restored.