Question

Q.1) Define quantum numbers and explain
its type also.
[5]​

Answer 1

Answer:

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Explanation:

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Answer 2

Answer:

The set of numbers used to describe the position and energy of the electron in an atom are called quantum numbers.

→ There are four quantum numbers, namely, principal, azimuthal, magnetic and spin quantum numbers

Explanation:

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 is described by it, a larger value of the principal quantum number implies a greater distance between the electron and the nucleus (which, in turn, implies a greater atomic size).

• 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.

Azimuthal Quantum Number (Orbital Angular Momentum Quantum Number)

• 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.

3rd quantum number in attachment

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 ↓.

• The value of the electron spin quantum number determines whether the atom in question has the ability to produce a magnetic field. The value of ms can be generalized to ±½.