Question

A hydrogen atom is in the d-state. The values of m for this state are
A. $-1,0,1$
B. $-3,-1,0,1,3$
C. $2,1,0$
D. $-2,-1,0,1,2$

Answer 1

Hint: To describe the energy and position of an electron in an atom, set of numbers called quantum numbers are used. In order to describe the state of electrons in an atom, the principal quantum number is used. It can have the value of any natural number. Apart from that, the shape of the orbital is described by the angular quantum number.

Complete step by step answer:
Step I:
The principal quantum number is denoted by $n$. The shells in principal quantum number are $K,L,M,N$. On the other hand, the angular momentum quantum number is denoted by the symbol $l$ and its value depends on the principal quantum number.

Step II:
The value of angular quantum number indicates the subshells as $s,p,d,f$. Its value lies between $n = 0,1,2.....n - 1$.
After the angular quantum number, there is a magnetic quantum number that describes the total number of orbitals in the subshell . It is denoted by ${m_l}$. Its value depends on angular quantum number and values are given by $2l + 1$.

Step III:
The possible values of m will be
${m_l} = - 1,....0,.... + 1$
Step IV:
When a hydrogen atom is in the d-state then the value of $l = 2$
So the number of orbitals will be $2l + 1$
Or $2(2) + 1 = 5$
Step V:
Therefore, m can have five possible values and they are $ - 2, - 1,0,1,2$

Therefore, the correct option is D.

Note:
It is to be noted that the angular momentum quantum number is also known as azimuthal quantum number. It describes the orbital angular momentum for an orbital. Since the electrons in an atom move around a circular orbit so azimuthal quantum number is given by relation $mvr$.