Question

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

Answer 1

Hint: We have to know that a quantum number is a value that is utilized while portraying the energy levels accessible to particles and atoms. An electron in an iota or particle has four quantum numbers to portray its state and yield answers for the Schrodinger wave condition for the hydrogen molecule.

Complete answer:
Quantum numbers are an approach to depict the discrete states that a molecule can hold. These would then be able to be utilized for answers for the Schrodinger condition.
Principle quantum number $\left( n \right)$ , this assigns the size of the orbital, additionally called the shell. The bigger the incentive for $\left( n \right)$ , the more noteworthy the normal distance of an electron in the orbital from the core and accordingly the bigger the orbital. From the condition that characterizes the line range of Hydrogen, we can likewise realize that the incentive for n addresses energy levels.
Angular momentum quantum number $\left( l \right)$ this depicts the state of the orbital, however once more, you can relate it back to the intermittent table. The upsides of l are whole numbers that rely upon the worth of the central quantum number, n. For some random worth of n, the conceivable scope of qualities for one go from zero to $n - 1$ . In the event that $n = 1$ , there's only one potential worth of one; that is, zero ($n - 1$ where, $n = 1$ ). On the off chance that $n = 2$ , there's two qualities for $1:0$ , and $1$ . On the off chance that $n = 3$ , one has three qualities: zero, one, and two.
Magnetic quantum number $\left( {ml} \right)$ this depicts the direction of the orbital in space, or the heading along the tomahawks wherein it faces. Inside a sub-shell, the worth of this relies upon the worth of one. For a specific worth of $l$ , there are $\left( {2l + 1} \right)$ indispensable qualities, or $ - 1,...0,... + 1$ .

Note:
We have to know that the initial three quantum numbers are the vital quantum number, the azimuthal quantum number, and the magnetic quantum number. The key quantum number indicates the energy shell level of the electron. The azimuthal quantum number indicates the subshell of the electron.