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QUESTION: 1

**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?**

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 = a_{0}) and then falls thus (c) is correct.

QUESTION: 2

For 2s-orbital electron, radial probability density R^{2} as function of r (distance) is given by

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

For an electron in 2p-orbital, radial probability function 4πr^{2}R^{2} as a function of r is given by

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

C onsider the following figures A and B indicating distribution of charge density (electron probability ) with distance r

Select the correct statement(s).

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

Select the correct statement(s).

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

Which orbital gives an electron, a greater probability being found close to the nucleus?

Solution:

3s is spherically symmetrical and its electron density is maximum at the nucleus. It decreases with r.

QUESTION: 7

Hamiltonian operator is the sum of two energy operators. These are

Solution:

H = T + V

QUESTION: 8

Angular nodes in 4s- suborbit is equal to radial nodes in

Solution:

Angular nodes in 4s = 0

QUESTION: 9

at any point is proportional to

Solution:

Radial probability density = 4πr^{2} of find in g the electron within the volume of a very thin spherical shell at a distance r from nucleus.

QUESTION: 10

There is formation of in all five nodes (including terminal nodes) in a string of 12 cm. Thus, wavelength of the waves formed is

Solution:

For n nodes in a string

QUESTION: 11

For x -axis , wave function () can be written as

Thus, Schrodinger wave equation along x-axis can be written as :

Solution:

QUESTION: 12

The Schrodinger wave equation for H-atom is

where, a_{0} is Bohr’s radius. If radial node in 2s is at distance r_{0}, then

Solution:

*Multiple options can be correct

QUESTION: 13

**Direction (Q. Nos. 13-15) This section contains 3 multiple choice questions. Each question has four choices (a), (b), (c) and (d), out of which ONE or MORE THANT ONE is correct.**

**Q. Which of the following properties can be described by wave function ** **?**

Solution:

The wave function describ es properties of the orbital and the electron that occupies the orbital

(a) Type of orbital is described : true

(b) Energy of electron : true

(c) Shape of the orbital: true

(d) Probability: true

*Multiple options can be correct

QUESTION: 14

As compared to 1s electron of H-atom in ground state, which of the following properties appear(s) in the radial probability density of 2s electron of H-atom in first excited state?

Solution:

For2s-electron of H-atom (first excited state)

For 1s-electron of H-atom in ground state

At point Ar = a_{0} r at point Br > a_{0}

(a) True (b) True (c) True (d) True

*Multiple options can be correct

QUESTION: 15

Radial probability density in the occupied orbital of a hydrogen atom in the ground state (1s) is given below

Solution:

Radial probability increases as r increase reaches a maximum value when r = a0 (Bohr’s radius) and then falls. When radial probability is very small.

Thus, (a) and (c) are true.

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