(d) Which of the following sets of quantum numbers is not permitted? Select all that apply.
2,1,1,-1/2
1,1,0,-1/2
2,-1,1,-1/2
3,2,1,1/2
Pls pls pls help me :( x
right!!!
To determine which sets of quantum numbers are not permitted, we need to consider the restrictions on each quantum number:
1. Principal Quantum Number (n): Represents the energy level or shell of an electron. It must be a positive integer (1, 2, 3, etc.).
2. Angular Momentum Quantum Number (l): Determines the shape of the orbital. It can have values from 0 to (n-1).
3. Magnetic Quantum Number (ml): Specifies the orientation or direction of the orbital. It can have values from -l to +l, including 0.
4. Spin Quantum Number (ms): Describes the spin state of an electron. It can have only two values: +1/2 (spin-up) or -1/2 (spin-down).
Let's evaluate each set of quantum numbers:
a) 2,1,1,-1/2
- Principal Quantum Number (n) = 2: Permitted since it's a positive integer.
- Angular Momentum Quantum Number (l) = 1: Permitted since it's within the range of 0 to (n-1).
- Magnetic Quantum Number (ml) = 1: Permitted since it's within the range of -l to +l.
- Spin Quantum Number (ms) = -1/2: Permitted since it's either +1/2 or -1/2.
This set of quantum numbers is permitted.
b) 1,1,0,-1/2
- Principal Quantum Number (n) = 1: Permitted since it's a positive integer.
- Angular Momentum Quantum Number (l) = 1: Permitted since it's within the range of 0 to (n-1).
- Magnetic Quantum Number (ml) = 0: Permitted since it's within the range of -l to +l.
- Spin Quantum Number (ms) = -1/2: Permitted since it's either +1/2 or -1/2.
This set of quantum numbers is permitted.
c) 2,-1,1,-1/2
- Principal Quantum Number (n) = 2: Permitted since it's a positive integer.
- Angular Momentum Quantum Number (l) = -1: Not permitted since it must be within the range of 0 to (n-1).
This set of quantum numbers is not permitted.
d) 3,2,1,1/2
- Principal Quantum Number (n) = 3: Permitted since it's a positive integer.
- Angular Momentum Quantum Number (l) = 2: Permitted since it's within the range of 0 to (n-1).
- Magnetic Quantum Number (ml) = 1: Permitted since it's within the range of -l to +l.
- Spin Quantum Number (ms) = 1/2: Permitted since it's either +1/2 or -1/2.
This set of quantum numbers is permitted.
Therefore, the set of quantum numbers that is not permitted is c) 2,-1,1,-1/2.
To determine which set of quantum numbers is not permitted, we need to first understand the rules for assigning quantum numbers. Quantum numbers describe the energy, shape, orientation, and spin of an electron within an atom.
There are four types of quantum numbers: principal quantum number (n), azimuthal quantum number (l), magnetic quantum number (mₗ), and spin quantum number (mₛ).
1. Principal quantum number (n): It describes the energy level or shell in which the electron is located. The values of n are positive integers (1, 2, 3, ...).
2. Azimuthal quantum number (l): It determines the shape of the orbital and can have integer values ranging from 0 to (n - 1). The possible values of l for a given value of n are 0, 1, 2, ..., (n - 1).
3. Magnetic quantum number (mₗ): It describes the orientation in space of the orbital, ranging from -l to +l. The values of mₗ are integers.
4. Spin quantum number (mₛ): It represents the intrinsic angular momentum or spin of the electron and can have two values: +1/2 (spin-up) or -1/2 (spin-down).
Now, let's evaluate each set of quantum numbers:
1. Set 2,1,1,-1/2: This set is valid, as all the values fall within the permitted ranges for n, l, mₗ, and mₛ.
2. Set 1,1,0,-1/2: This set is valid as well, as all the values fall within the permitted ranges.
3. Set 2,-1,1,-1/2: The value of l (-1) is not permitted since l must range from 0 to (n - 1), where n = 2. Therefore, this set is not permitted.
4. Set 3,2,1,1/2: This set is valid as all the values fall within the permitted ranges.
To summarize, the set of quantum numbers that is not permitted is 2,-1,1,-1/2.
1,1,0,-1/2
2,-1,1,-1/2
answer by amar chauhan