Name: Dual Nature of Light and Matter
Uploaded: 2019-07-19
Duration: 7 min 31 s
Description: Light has a dual nature. It is both a wave and a particle. Explore this video about the wave and particle nature of light and the wavelength corresponding to...

Question

How are the quantum numbers

n, l

and

m_{l}

arrived at? Explain the significance of these quantum numbers.

Accepted Answer

The three quantum numbers $n, l$ and $m_{l}$ are solutions to the Schrodinger wave equation. These quantum numbers give various information about an electron.

(a) The principal quantum number $(n)$ represents the shell number and tells us about the size and energy of the shell in which the electron is present.

(b) The azimuthal quantum number $(l)$ represents subshells. There are four subshells $s, p, d$ and $f$ , each having a different shape. For a given value of $n$ , the possible values of $l$ are from $0$ to $n - 1$ .

Subshell $l$ value Shape

$s$ $0$ Spherical

$p$ $1$ Dumbbell

$d$ $2$ Double dumbbell

$f$ $3$ Complex shape

(c) The magnetic quantum number $(m_{l})$ represents number of orbitals in a subshell and their orientations. For a given value of $l$ , the $m_{l}$ value ranges from $- l$ to $n, l$ . Each $m_{l}$ value represents a different orientation.

Subshell $l$ value $m_{l}$ values

$s$ $0$ $0$

$p$ $1$ $- 1, 0, 1$

$d$ $2$ $- 2, - 1, 0, 1, 2$

$f$ $3$ $- 3, - 2, - 1, 0, 1, 2, 3$

For an $s$ -subshell, only a single orientation is possible.
For a $p$ -subshell, three orientations are possible, representing the three $p$ -orbitals $p_{x}, p_{y}$ and $p_{z}$ .
For a $d$ -subshell, five orientations are possible, representing the five $d$ -orbitals $d_{xy}, d_{xz}, d_{yz}, d_{x^{2} - y^{2}}$ and $d_{z^{2}}$ .
For an $f$ -subshell, seven orientations are possible, each representing a different $f$ -orbital.

How are the quantum numbers $n, l$ and $m_{l}$ arrived at? Explain the significance of these quantum numbers.

Important Questions on Atomic Structure

Learn and Prepare for any exam you want !

How are the quantum numbers n, l and ml arrived at? Explain the significance of these quantum numbers.

Important Questions on Atomic Structure

Learn and Prepare for any exam you want !

How are the quantum numbers $n, l$ and $m_{l}$ arrived at? Explain the significance of these quantum numbers.