Question

How many quantum numbers are required to identify the orbital?

Answer 1

Hint: The trajectory and acceleration of an electron in an atom can be described using quantum numbers. When all of the electrons in an atom's quantum numbers are added together, the Schrodinger equation must be satisfied.

Complete answer:
Quantum numbers are a sequence of numbers that represent the position and energy of an electron in an atom. Principal, azimuthal, magnetic, and spin quantum numbers are the four types of quantum numbers.
Quantum numbers define the values of a quantum system's conserved quantities. Electronic quantum numbers (quantum numbers that describe electrons) can be described as a set of numerical values that provide Schrodinger wave equation solutions for hydrogen atoms.
The following four quantum numbers can be used to fully explain all of the characteristics of an atom's electrons:
n is the principal quantum number.
The quantum number of orbital angular momentum (also known as the azimuthal quantum number) is denoted by the letter l.
\[{m_l}\] stands for magnetic quantum number.
\[{m_s}\] stands for the electron spin quantum number.
Principal Quantum Number:
The symbol ‘$n$' stands for principal quantum numbers. They designate the atom's primary electron shell. Since it describes the most likely distance between the nucleus and the electrons, a larger value of the principal quantum number denotes a smaller distance between the nucleus and the electrons (which, in turn, implies a greater atomic size).
Any integer with a positive value equal to or greater than one can be used as the principal quantum number's value. The value $n=1$ denotes an atom's innermost electron shell, which refers to an electron's lowest energy state (or ground state).
Azimuthal Quantum Number (Orbital Angular Momentum Quantum Number):
The shape of an orbital is defined by the azimuthal (or orbital angular momentum) quantum number. Its value is proportional to the total number of angular nodes in the orbital and is denoted by the symbol $l.$
The azimuthal quantum number may mean an $s, p, d,$ or $f$ subshell, all of which have different shapes. This value is determined by (and limited by) the principal quantum number, i.e. the azimuthal quantum number varies between $0$ and $1. (n-1)$.
Magnetic Quantum Number:
The magnetic quantum number determines the cumulative number of orbitals in a subshell as well as their orientation. The symbol \[{m_l}\] is used to represent it. This number represents the projection of the orbital angular momentum onto a given axis.
The azimuthal (or orbital angular momentum) quantum number determines the magnitude of the magnetic quantum number. The value of ml for a given value of l is in the range of $-l$ to $+l$. As a result, it is indirectly affected by the value of $n$.
Electron Spin Quantum Number:
The values of $n, l,$ and $ml$ have no bearing on the electron spin quantum number. The symbol \[{m_s}\] represents the value of this figure, which indicates the direction in which the electron is spinning.
The value of \[{m_s}\] provides information about the electron's spin position. The electron spin quantum number has two potential values: $\dfrac{+1}{2}$ and $\dfrac{-1}{2}$.
For an Orbital:
Three quantum numbers, the principal quantum number, azimuthal quantum number, and magnetic quantum number, are used to identify an orbital.
Quantum numbers are a sequence of numbers that represent the position and energy of an electron in an atom.
An orbital's three quantum numbers ($n, l$, and $m$) are all integers: $0, 1, 2, 3$, and so on.
It is impossible for the principal quantum number ($n$) to be $0$. As a result, the permitted values of $n$ are $1, 2, 3, 4,$ and so on.
Any integer between $0$ and $n – 1$ can be used as the angular quantum number ($l$). For eg, if $n = 3$, $l$ may be $0, 1$, or $2$.
Any integer between $–l$ and $+l$ can be used as the magnetic quantum number ($m$). If $l = 2$, $m$ can be any of the following values: $-2, -1, 0, +1,$ or $+2$.

Note:
The symbol ‘n' stands for principal quantum numbers. They designate the atom's primary electron shell. Since it describes the most likely distance between the nucleus and the electrons, a larger value of the principal quantum number denotes a smaller distance between the nucleus and the electrons (which, in turn, implies a greater atomic size).