The set of a quantum number that represents degenerate orbitals is: 
 
a. \( \small{n=3, \ell=2, m=0, s=\frac{-1}{2} \,\& \ \,n=3, \ell=2, m=-1, s=\frac{+1}{2}}\)
b. \(\small{n=2, \ell=1, m=1 , \ s=\frac{-1}{2}\, \&\, \ n=3, \ell=1, m=1 \mathrm{~s}=\frac{+1}{2}}\)
c. \(\small{n=4, \ell=2, m=-1, s=\frac{1}{2}\, \&\, \ n=3, \ell=2, m=-1, s=\frac{1}{2}}\)

1. a 
2. b 
3. c 
4. a, b 
Subtopic:  Quantum Numbers & Schrodinger Wave Equation |
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The total energy of 1 mol of photons in J/mol having \(\lambda = 600 \ nm \) is:

Given: \(h = 6.62 \times 10^{-34} \mathrm{~J} \ \mathrm{sec}, \mathrm{c}=3 \times 10^{8} \mathrm{~m \ s}^{-1}\)

1. \(2 \times 10^5 J/mol\)
2. \(6.64 \times 10^8 J/mol\)
3. \(1.24 \times 10^4 J/mol\)
4. \(1.24 \times 10^8 J/mol\)
Subtopic:  Electromagnetic Radiation |
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Given that the threshold frequency of the metal is \(1.4 \times 10^{15}sec^{-1}\), what is the minimum energy required to eject a photoelectron from the metal?
[given: \(h = 6.6 \times 10^{-34} J sec\)]

1. \(9.24 \times 10^{-19}J \)
2. \(9.24 \times 10^{-18}J \)
3. \(4.62 \times 10^{-19}J \)
4. \(4.62 \times 10^{-18}J \)
Subtopic:  Photo Electric Effect |
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Using the following statements, identify the correct set of statements:
(i). n (principal quantum number) can have values 1, 2, 3, 4, .......
(ii). The number of orbitals for a given value of l is (2l+1).
(iii). The value of spin quantum numbers is always \(\pm\frac12\).
(iv). For l=5, the total number of orbitals is 9.

1.  (i), (ii), (iii)
2.  (i), (ii), (iv)
3.  (i), (ii), (iii), (iv)
4.  (i), (iii), (iv)
Subtopic:  Quantum Numbers & Schrodinger Wave Equation |
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The plots of radial distribution functions for various orbitals of hydrogen atom against 'r' are given below:

a.

 

b.

 

c. 

d.

The correct plot for 3s orbital is:

1. (B)

2. (A)

3. (D)

4. (C)

Subtopic:  Quantum Numbers & Schrodinger Wave Equation |
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A proton and a Li3+ nucleus are accelerated by the same potential. If λLi3+ and λp denote the de-Broglie wavelengths of Li3+ and proton respectively, then the value of \(\frac{\lambda _{Li^{3+}}}{\lambda _{p}}\) is x × 10−1. The value of x is:

(Rounded off to the nearest integer)

(Mass of Li3+ = 8.3 the mass of a proton) 

1. 4 
2. 6 
3. 2
4. 8
 

Subtopic:  De Broglie Equation |
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The quantum number of four electrons are given below : 

I.  n = 4, l=2 , m= -2, ms\(-\frac{1}{2}\)
II.  n=3, l=2, ml = 1, m\(+\frac{1}{2}\)
III.  n=4 , l=1, ml = 0, m\(+\frac{1}{2}\)
IV.  n=3, l=1, ml=1, ms=\(-\frac{1}{2}\)


The correct order of their increasing energies will be:

1. I < III < II < IV
2. IV < II < III < I
3. I < II < III < IV
4. IV < III < II < I

Subtopic:  Shell & Subshell |
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The graph between ψ2 and r (radial distance) is shown below. This represents:

1. 3s orbital 2. 2s orbital
3. 2p orbital 4. 1s orbital
Subtopic:  Quantum Numbers & Schrodinger Wave Equation |
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The radius of the second Bohr orbit for hydrogen atom is:

(Planck's Const. h = 6.6262 × 10–34 Js; mass of electron = 9.1091 × 10–31 kg; charge of electron e = 1.60210 ×10–19 C; permittivity of vaccum 0 = 8.854185 ×10–12 kg–1m–3A2)

1. 0.529 Å

2. 2.12 Å

3. 1.65 Å

4. 7.76 Å

Subtopic:  Bohr's Theory |
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The correct set of four quantum numbers for the valence electrons of rubidium atom (Z = 37) is -

1. 5, 1, 0 + 12

2. 5, 1, 1 + 12

3. 5, 0, 1 +12

4. 5, 0, 0 + 12

Subtopic:  Quantum Numbers & Schrodinger Wave Equation |
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