Quantum Mechanical Model Of Atom

Step 1: Definition
Degenerate orbitals are orbitals belonging to the same subshell that have the same energy level.
Step 2: Analysis
In molecular orbital theory for homonuclear diatomic molecules, the and molecular orbitals are formed from the same atomic subshells and are symmetric.
Step 3: Conclusion
Because they have nearly equal energy levels, they are considered degenerate.
Final Answer: (B)

Step 1: Understanding quantum numbers.
The four quantum numbers , , , and describe the properties of electrons in an atom: - is the principal quantum number (n = 1, 2, 3, ...), - is the azimuthal quantum number (l = 0 to ), - is the magnetic quantum number (m = - to ), - is the spin quantum number (s = ).

Step 2: Analyze the given options.
- (1) : This set is not permitted because for , the azimuthal quantum number must be between 0 and 2, but here , which violates the rule. - (2) : This is a valid set of quantum numbers. - (3) : This is also a valid set of quantum numbers. - (4) : This is a valid set of quantum numbers.

Step 3: Conclusion.
The correct answer is (1) because cannot be equal to 3 when .

Step 1: Understanding the definition of an orbital.
An orbital refers to the region in an atom where there is a high probability of finding an electron. It is not a fixed path like a planet orbiting the Sun. Instead, it is a three-dimensional probability distribution of where the electron is likely to be found.

Step 2: Analyze the options.
- (1) Circular path around the nucleus: This is incorrect, as electrons do not move in fixed paths but in orbitals.
- (2) Space around the nucleus where the probability of finding the electron is maximum: This is the correct definition of an orbital.
- (3) Amplitude of electron’s wave: This is related to the wave function, but it is not the definition of an orbital.
- (4) None of the above: This is incorrect, as option (2) is the correct definition.

Step 3: Conclusion.
The correct answer is (2) space around the nucleus where the probability of finding the electron is maximum.

Step 1: Understanding the Concept:
Electronic configuration of Sc ( ): .
Step 2: Detailed Explanation:
Order of filling: 1s (2 e ), 2s (2 e ), 2p (6 e ), 3s (2 e ), 3p (6 e ), 4s (2 e ).
19th electron enters 4s orbital. For 4s: .
Step 3: Final Answer:
Thus, quantum numbers: .

Step 1: Understanding the Concept:
Tap water contains Cl ions. White turbidity soluble in NH indicates AgCl. Brown ring test confirms NO .
Step 2: Detailed Explanation:
AgNO + tap water (Cl ) AgCl (white turbidity). AgCl dissolves in NH forming [Ag(NH ) ] .
Heating AgNO : 2AgNO 2Ag + 2NO + O .
Brown ring test: NO + 3Fe + 4H NO + 3Fe + 2H O; NO + Fe [Fe(NO)] (brown).
Step 3: Final Answer:
Thus, (A) = AgNO .

Concept:

Step 1: Given angular nodes = 2, hence (d-orbital).

Step 2: Use radial node formula: .


Step 3: Thus orbital corresponds to , .
Conclusion:
Orbital = 4d

Concept: Quantum numbers define the state of an electron:
• = principal quantum number
• = azimuthal quantum number
• = magnetic quantum number
• = spin quantum number

Step 1: Write electronic configuration of Br (Z=35):


Step 2: Last electron enters 4p orbital .

Step 3: Possible values: and last electron pairs up .

Step 4: Valid set matching these values is (4,1,1, ).
Conclusion:
Correct quantum numbers are (4,1,1, )

Concept: Allowed Quantum Numbers
• Principal quantum number:
• Azimuthal quantum number:
• Magnetic quantum number:
• Spin quantum number:

Step 1: Check option (A) But given: Hence, option (A) is not possible.

Step 2: Check remaining options (B), (C), (D) all satisfy: So they are valid. Final Answer: A

Concept: Quantum Numbers
• Principal quantum number:
• Azimuthal quantum number:
• Magnetic quantum number:

Step 1: Check each option (A) Allowed since (B) Allowed since (C) Here , so: But given → not allowed (D) Allowed since Final Answer: C

Concept: Use rule:

Step 1: Calculate values.


Step 2: Tie-breaking.
Lower → lower energy:

Step 3: Final order.