What is quantum number? How many types of quantum number are there?
Answers
Answer:
group of no.s which give complete address of an electron and there are four type of qu. no.s
Answer:
Quantum numbers can be used to describe the trajectory and the movement of an electron in an atom. The quantum numbers of all the electrons in a given atom, when combined, must comply with the Schrodinger equation.
What are Quantum Numbers?
The values of the conserved quantities of a quantum system are given by quantum numbers. Electronic quantum numbers (the quantum numbers describing electrons) can be defined as a group of numerical values which provide solutions that are acceptable by the Schrodinger wave equation for hydrogen atoms.
A brief description of each of these numbers in the set of four quantum numbers that describe the unique quantum state of an electron in atomic physics can be found in the next subsection.
The 4 Quantum Numbers that Describe an Electron
When the characteristics of an electron must be described in compliance with the Schrodinger wave equation, a total of four quantum numbers are used.
Principal Quantum Number
Principal quantum numbers are denoted by the symbol ‘n’. They designate the principal electron shell of the atom. Since the most probable distance between the nucleus and the electrons are described by it, a larger value of the principal quantum number implies a greater distance between the electron and the nucleus .
The value of the principal quantum number can be any integer with a positive value that is equal to or greater than one. The value n=1 denotes the innermost electron shell of an atom, which corresponds to the lowest energy state (or the ground state) of an electron.
Thus, it can be understood that the principal quantum number, n, cannot have a negative value or be equal to zero because it is not possible for an atom to have a negative value or no value for a principal shell.
The azimuthal (or orbital angular momentum) quantum number describes the shape of a given orbital. It is denoted by the symbol ‘l’ and its value is equal to the total number of angular nodes in the orbital.
A value of the azimuthal quantum number can indicate either an s, p, d, or f subshell which vary in shapes. This value depends on (and is capped by) the value of the principal quantum number, i.e. the value of the azimuthal quantum number ranges between 0 and (n-1).
For example, if n =3, the azimuthal quantum number can take on the following values – 0,1, and 2. When l=0, the resulting subshell is an ‘s’ subshell. Similarly, when l=1 and l=2, the resulting subshells are ‘p’ and ‘d’ subshells (respectively). Therefore, when n=3, the three possible subshells are 3s, 3p, and 3d.
Magnetic Quantum Number
The total number of orbitals in a subshell and the orientation of these orbitals are determined by the magnetic quantum number. It is denoted by the symbol ‘ml’. This number yields the projection of the angular momentum corresponding to the orbital along a given axis.
Orbitals as per Quantum Numbers
The value of the magnetic quantum number is dependant on the value of the azimuthal (or orbital angular momentum) quantum number. For a given value of l, the value of ml ranges between the interval -l to +l. Therefore, it indirectly depends on the value of n.
For example, if n = 4 and l = 3 in an atom, the possible values of the magnetic quantum number are -3, -2, -1, 0, +1, +2, and +3.
Azimuthal Quantum Number Value Corresponding Number of Orbitals (2l + 1) Possible Values of ml
0 (‘s’ subshell) 2*0 + 1 = 1 0
1 (‘p’ subshell) 2*1 + 1 = 3 -1, 0, and 1
2 (‘d’ subshell) 2*2 + 1 = 5 -2, -1, 0, 1, and 2
3 (‘f’ subshell) 2*3 + 1 = 7 -3, -2, -1, 0, 1, 2, and 3
The total number of orbitals in a given subshell is a function of the ‘l’ value of that orbital. It is given by the formula (2l + 1). For example, the ‘3d’ subshell (n=3, l=2) contains 5 orbitals (2*2 + 1). Each orbital can accommodate 2 electrons. Therefore, the 3d subshell can hold a total of 10 electrons.
Electron Spin Quantum Number
The electron spin quantum number is independent of the values of n, l, and ml. The value of this number gives insight into the direction in which the electron is spinning, and is denoted by the symbol ms.
The value of ms offers insight into the direction in which the electron is spinning. The possible values of the electron spin quantum number are +½ and -½.
The positive value of ms implies an upward spin on the electron which is also called ‘spin up’ and is denoted by the symbol ↑. If ms has a negative value, the electron in question is said to have a downward spin, or a ‘spin down’, which is given by the symbol ↓.
Explanation: