Explain the significance of three quantum numbers in predicting the positions of an electron in an orbit .

Explanation

Each electron in an atom is described by a set of three quantum numbers n,l and `m_l`.
1. Principal quantum number (n) : The principal quantum number is used to describe the size and energy of the main shell. It is denoted by 'n'. 'n' has positive integer values of 1,2,3,............. It is used to know the number of orbitals `(n^2)` and electrons in an orbit. `(2n^2)`.

As 'n' increases the shells becomes larger and the electrons in those shells are farther from the nucleus and their energies increases.
2. The angular-momentum quantum number(l) : 'l' has integer values from '0' to n-1, for each value of 'n'. Each 'l' value represents one sub-shell. It is used to describe the shape of an orbit.

3. The magnetic quantum number `(m_l)` : The magnetic quantum number `(m_l)` has integer values between -l and +l including zero.
If l=0, the possible `m_l` value is 1. l=1 , the possible `m_l` value is -1, 0 and 1.

Thus for a certain value of l, there are (2l+1) integer values of `m_l`.
These values describe the orientation of the orbital in space relative to the other orbitals in the atom.
Ex : When l=1,(2l+1)=3, that means `m_l` has 3 values namely -1,0,1 or three p orbitals, with different orientations along x,y,z axes, labelled as `p_x,p^y" and " p_z` orbitals.
Predicting the position of an edectron in an atom : If the values of n,l and `m_l` are 2,1,-1 respectively the electron is present in `2p_x` orbital in L - shell.
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