Question

How many d-orbitals can there be in one energy level?

Answer 1

Hint: Electrons exist around the nucleus in specific orbits. The orbitals cannot be of any distance from the nucleus. These orbits are called levels, which are further divided into sublevels. There are 4 common sub levels i.e. s,p,d,f sublevels. S orbital has 2 electrons, p has 6 electrons and d has 10 electrons.

Complete answer:
The no. of orbitals and the positions of the electron in an atom is determined by the 4 quantum numbers.
First is the principal quantum number (n): This is denoted by the letter ‘n’ and is the principal energy level. This number tells us about the size of the orbital and also its energy. As n increases the energy also increases, and the electron moves far off from the nucleus. This quantum number has only integral values i.e., n = 1 (K), 2(L), 3(M), 4(N)….
Second is the azimuthal quantum number: It is denoted by the letter ‘l’. It denotes the subshells and the shape of the electron cloud. The value of l is related to n. The value of l can take any value from 0 to a maximum of $(n - 1)$ . The values of l can be $l = 0,1,2,3,4..$This represents the subshells s, p, d, f respectively. Hence the value of l for d-orbital is 2.
Therefore, the value of n for d-orbital should be $n \geqslant 3$. Below 3 the orbit doesn’t contain a d-subshell.
This is the magnetic quantum number: It is denoted by ‘m’. Used to determine the no. of orbital in a subshell. This number has an integral value including 0 from \[ - l{\text{ to }} + l\]. For d-orbital (l= 2) the value of m can range from -2 to +2. Hence, $m = - 2, - 1,0, + 1, + 2$
Therefore, the d subshell has 5 orbitals.

Note:
Apart from these there is a spin quantum number which designates the spin of the electron in a particular orbital. The value can be either $ - 1/2{\text{ or }} + 1/2$. Remember that no electron in a particular shell has all quantum numbers the same. Every electron has a unique set of quantum numbers.