# The maximum number of electrons that can have principal quantum number n = 2 and spin quantum number ms = -1/2 is

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The maximum number of electrons that can have principal quantum number n = 2 and spin quantum number ms = -1/2 is
1. 1
2. 2
3. 4
4. 3

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Correct Answer - Option 3 : 4

Concept:

Quantum Mechanical Model of Atom

Quantum mechanics is a theoretical science that deals with the study of the motions of microscopic objects that have both observable wave-like and particle-like properties.

A large number of orbitals are possible in an atom. Qualitatively these orbitals can be distinguished by their size, shape and orientation. An orbital of smaller size means there is more chance of finding the electron near the nucleus.

Each orbital is designated by three quantum numbers labeled as n, l, and ml. The principal quantum number ‘n’ is a positive integer with a value of n = 1, 2, 3.......

• The principal quantum number determines the size and to large extent the energy of the orbital. Size of orbital increases with an increase of principal quantum number ‘n’. In other words, the electron will be located away from the nucleus. Also, the energy of the orbital will increase with an increase of n.
• Azimuthal quantum number, ‘l’ is also known as orbital angular momentum or subsidiary quantum number. It defines the three-dimensional shape of the orbital. For a given value of n, l can have n values ranging from 0 to n – 1, that is, for a given value of n, the possible value of l are: l = 0, 1, 2, .......... (n - 1)
• Magnetic orbital quantum number ml gives information about the spatial orientation of the orbital with respect to standard set of co-ordinate axis. It can be any integer between -l and +l i.e. 2l + 1 values of ml are possible.
• The spin quantum number (s): An electron can spin either in the clockwise direction or in the anticlockwise direction, therefore, for any particular value of the magnetic quantum number, the spin quantum number can have two values, i.e., +1/2 and –1/2
 Quantum Number Symbol Values Principal n 1, 2, ... Angular Momentum l 0,1, 2, ……... n - 1 Magnetic m -l to +l Spin Magnetic s +1/2, -1/2

Calculation:

Given principal quantum number n = 2 and spin quantum number ms = -1/2,

⇒ n = 2  and ms = -1/2;

n = 2 ⇒ l = 0,1

l = 0, 1 ⇒ ml = -1, 0, 1;

Total number of orbitals = n2 = 4;

2s - n = 2, l = 0, ml = 0;

2px - n = 2, l = 1, ml = -1;

2py - n = 2, l = 1, ml = 0;

2py - n = 2, l = 1, ml = -1;

Lets assume all the four orbitals are filled with one electron each with spin quantum number -1/4...

∴, maximum number of electrons possible are 4