Question

What is one possible set of quantum numbers for a 4d orbital?

Answer 1

Hint: Electrons have a unique set of quantum numbers, which means that two electrons can share three, two or one quantum numbers but never all four quantum numbers. Quantum number is the set of four integers required to define an electron completely in an atom called quantum number. Quantum system can have one or more quantum numbers.

Complete answer:
Principle quantum number (n): It describes the shape, size and energy of the shell to which electron belong, it is denoted by n, where,
$n=1,2,3,4............\mathrm{\infty }$
Azimuthal quantum number(l):it determines the shape of an electron cloud and number of subshells in a shell. The value of l lies between 0 to n-1 i.e., l=0 to n-1
Magnetic quantum number(m): it determines the orientation of sub shells. The value of m can have from –l to +l including zero. i.e., $m=2l+1$
Spin quantum number(s): it represents the direction of electron spin around its own axis. It has $S=+{\displaystyle \frac{1}{2}}$ for clockwise direction and $S=-{\displaystyle \frac{1}{2}}$ for anticlockwise direction
The value of principal quantum number for a 4d orbital will always be 4 and the value azimuthal quantum number will always be equal to 2.for 4d orbitals the values of the magnetic quantum number range from –l to l, so the values of ml are -2, -1, 0, 1, and 2. And the values of mS are always ${\displaystyle \frac{1}{2}}$ and $-{\displaystyle \frac{1}{2}}$ . For 4d orbital a total of 10 possible variations of quantum numbers are possible and one such variation is $n=4,l=2,ml=0,ms={\displaystyle \frac{1}{2}}$

Note: Quantum numbers which describes values of conserved quantities in the dynamics of a quantum system in chemistry and quantum physics and quantum numbers correspond to eigenvalues of operators that commute with the Hamiltonian-quantities which can be known with precision at the same time as the systems energy and their corresponding Eigenspaces.