Atomic Structure Test

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Atomic Structure Test - 22

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Question 1
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Direction (Q. Nos. 1-12) This section contains 12 multiple choice questions. Each question has four choices (a), (b), (c) and (d), out of which ONLY ONE option is correct.
Q.
Radial wave functio ns (R) of different orbitals are plotted. Which is/are correct graphs?

A

B

C

D
All of these

Solution

For 1s-orbital radial wave function (Ft) is maximum at r - 0, and falls rapidly as r increases thus, (a) correct.
For2s-orbital, radial wave function (R) is maximum at (r = 0), falls to zero and further decreases with r. There appears radial nodes. Thus (b) correct.
For2p-orbital, radial wave function is zero at r = 0, reaches maximum value (at r = a₀) and then falls thus (c) is correct.
Question 2
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For 2s-orbital electron, radial probability density R² as function of r (distance) is given by

A

B

C

D
all of these

Solution

Correct Answer : b
Explanation : (a) It represents R2 vs r for 1s
(b) It represents R2 vs r for2s
(c) It represents R2 vs r for 2p
Question 3
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For an electron in 2p-orbital, radial probability function 4πr²R² as a function of r is given by

A

B

C

D

Solution

(a) Describes radial wave function as a function of r for 1s
(b) Describes radial probability function as a function of r for 2s
(c) Describes radial wave function as a function r for 2s
(d) Describes radial probability function as a function of r for 2p
Question 4
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C onsider the following figures A and B indicating distribution of charge density (electron probability ) with distance r
Select the correct statement(s).

A
Both A and B are for 1s

B
Both A and B are for 2s

C
A is for 2s and B is for 1s

D
A is for 1s and B is for 2s

Solution

in case of 1s, falls as r increases thus, (A) is for 1s.
In case of 2s, is maximum in the vicinity o f the nucleus, falls to zero giving spherical nodes and then rises to second highest value. Thus, (6) is for2s
Question 5
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Select the correct statement(s).

A
| | measures the electron probability density at point in an atom

B
and | | vary as a function of the three coordinates r (radial), θ and ( (angular part)

C
Angular wave function ‘θ’ depends an only l and m, and is independent of n

D
All of the above are correct statements

Solution

Thus, is d e pendent on r true

(b) and | | are dependent on r, θ and : true
(c) Angular wave function is determined by /land m, and not by n: true
Question 6
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Which orbital gives an electron, a greater probability being found close to the nucleus?

A
3p

B
3d

C
3s

D
equal

Solution

3s is spherically symmetrical and its electron density is maximum at the nucleus. It decreases with r.
Question 7
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Hamiltonian operator is the sum of two energy operators. These are

A
mechanical and potential

B
kinetic and mechanical

C
kinetic and potential

D
thermal and potential

Solution

H = T + V
Question 8
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Angular nodes in 4s- suborbit is equal to radial nodes in

A
3d

B
2p

C
Both (A) and (B)

D
none of these

Solution

Angular nodes in 4s = 0
Question 9
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at any point is proportional to

A
the probability of finding the particle at that point

B
energy of the electron

C
radius of the orbital

D
(radius)^-1 of the orbital

Solution

Radial probability density = 4πr² of find in g the electron within the volume of a very thin spherical shell at a distance r from nucleus.
Question 10
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There is formation of in all five nodes (including terminal nodes) in a string of 12 cm. Thus, wavelength of the waves formed is

A
6.0 cm

B
4.8 cm

C
2.4 cm

D
1.2 cm

Solution

For n nodes in a string
Question 11
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For x -axis , wave function () can be written as
Thus, Schrodinger wave equation along x-axis can be written as :

A

B

C

D
None of the above

Solution
Question 12
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The Schrodinger wave equation for H-atom is
where, a₀ is Bohr’s radius. If radial node in 2s is at distance r₀, then

A

B

C

D

Solution