Question

How many values of ml are allowed for an electron in a 5f subshell??

Answer 1

There are 7 values ​​of ml are allowed for an electron in a 5f subshell namely: -3 -2, -1, 0, +1, +2, +3

Further explanation

In an atom, there are energy levels in the shell and subshell.This energy level is expressed in terms of electron configurations.

Writing the electron configuration starts from the lowest to the highest subshell's energy level. There are 4 sub-shells in an atom's shell, namely s, p, d, and f. The maximum number of electrons for each subshell is

• s: 2 electrons
• p: 6 electrons
• d: 10 electrons and
• f: 14 electrons

Electron filling in subshells using the following sequence:

1s², 2s², 2p⁶, 3s², 3p⁶, 4s², 3d¹⁰, 4p⁶, 5s², 4d¹⁰, 5p⁶, 6s², etc.

Each sub-shell also has orbitals drawn in the form of a square box in which there are electrons symbolized by half arrows.

Each orbital in an atom consists of 4 quantum numbers

• n is the principal quantum number.
• l is the angular momentum / azimuthal quantum number
• ml, the magnetic quantum number
• ms, the electron-spin quantum number

Value of n: positive integer

value of l: s = 0, p = 1, d = 2, f = 3

ml value: between -l to + l

ms value: +1/2 or -1/2

Determination of electron configurations based on principles:

• 1. Aufbau: Electrons occupy orbitals of the lowest energy level
• 2 Hund: electron fills orbitals with the same energy level
• 3. Pauli: there are no electrons that have 4 equal quantum numbers

So for 5f orbitals, the value of a possible quantum number is

n = 5;

l = 3 (f = 3);

m = -3 -2, -1, 0, +1, +2, +3;

s = + - 1/2

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Answer 2

The total number of   values for a given 5f subshell is $\boxed{\mathbf{7}}$ .

Further Explanation:

The size, energy, shape, and orientation of an orbital depend upon four quantum numbers. These quantum numbers are,

1. Principal Quantum Number (n): It denotes the principle electron shell. The values of n are a positive integer (1, 2, 3,    ).

2. Angular Momentum Quantum Number (l): It represents the shape of an orbital. The value of l is an integer from 0 to $\left( {n - 1}\right)$ .

3. Magnetic Quantum Number $\left( {{m_l}}\right)$: This quantum number represents the orientation of the orbital in space. The value of ${m_l}$ lie between  to  . The formula to calculate the value of ${m_l}$  is as follows:

${m_l} =  - l,( - l + 1),.....,0,1,2,.....,(l - 1),l$

Therefore, the total number of ${m_l}$  values for a given value of l is $2l + 1$ .

4. Electron Spin Quantum Number $({m_s})$: It represents the direction of electron spin. Its value can be $+ \frac{1}{2}$ or$- \frac{1}{2}$ .

The given subshell is 5f.

The value of the angular momentum quantum number (l) for f subshell is 3.(Refer to the table in the attached image)

Therefore, the total number of  ${m_l}$ values for a given 5f subshell can be calculated as,

$\begin{aligned}{\text{Total number of\; }}{{\text{m}}_l}{\text{ values}}&={\text{2}}\left( l \right){\text{ + 1}}\\&={\text{2}}\left( 3 \right){\text{ + 1}}\\&= {\mathbf{7}}\\\end{aligned}$

These values of ${m_l}$ lies between $- l$ to $+ l$ , therefore the values of ${m_l}$ for 5f are,

$- {\mathbf{3}},-{\mathbf{2}},-{\mathbf{1}},{\mathbf{0}},+{\mathbf{1}},+{\mathbf{2}},+ {\mathbf{3}}$

The total number of ${m_l}$ values for 5f subshell is 7.

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Answer details:

Grade: Senior School

Subject: Chemistry

Chapter: Structure of atom

Keywords: ml values, allowed, electrons in 5f subshell, angular momentum quantum number, principal quantum number, magnetic quantum number, electron spin quantum number.