Question

Which of the following quantum numbers is not derived from the Schrodinger wave equation?

A.principal
B.Azimuthal
C.Magnetic
D.Spin

Answer 1

Hint: We know that, to describe an electron completely we need four quantum numbers, they are, principal quantum number $\left( n \right)$, Azimuthal quantum number (l), magnetic quantum number $\left( {{m_l}} \right)$ and spin quantum number(s).

Complete step by step answer:
We know that, Schrodinger equation is written in the form of $\Psi $.

$\dfrac{{{d^2}\Psi }}{{d{x^2}}} + \dfrac{{{d^2}\Psi }}{{d{y^2}}} + \dfrac{{{d^2}\Psi }}{{d{z^2}}} + \dfrac{{8{\pi ^2}m}}{{{h^2}}} \times \left( {E - V} \right) \times \Psi = 0$

${\nabla ^2}\Psi + \dfrac{{8{\pi ^2}m}}{{{h^2}}}\left( {E - V} \right)\Psi = 0$


Here, $\Psi $ is amplitude of wave, E is energy (total ) of an electron, V is potential energy, m is mass of electron and h is Planck’s constant and $\dfrac{{{d^2}\Psi }}{{d{x^2}}}$is second derivative of $\Psi $ with respect to x.

On solving the equation, we get a set of quantum numbers. These quantum numbers describe energies of electrons in atoms. They also give information about orientation and shape of the most probable distribution of electrons around the nucleus. The quantum numbers derived from the Schrodinger equation are principal quantum number, Azimuthal quantum number and magnetic quantum number. But spin quantum number is not related to the Schrodinger equation. Spin quantum number is associated with the electron’s spin in doublets of the orbital.

Therefore, the quantum number which is not derived from the Schrodinger equation is spin quantum number.

Hence, option D is the correct answer.



Note:
Principal quantum number (n) indicates the principal shell of the electron. If n=1, that means electrons are present in the first principal shell. Value of n=1,2,3,4….
The angular quantum number (l) determines the shape of an orbital in which electrons are present.
Magnetic quantum number $\left( {{m_l}} \right)$ determines the orientation and number of orbitals.

Spin quantum number (s) indicates the direction of spin of electrons. The spin of an electron can be represented by either -1/2 or +1/2.