Question

The maximum number of electrons in p-orbital with $ n = 5 $ , $ m = 1 $ is;
 $ A) $ $ 6 $
 $ B) $ $ 2 $
 $ C) $ $ 14 $
 $ D) $ $ 10 $

Answer 1

Hint :Quantum numbers may be defined as a set of four numbers with the help of which we can get complete information about the electrons in an atom. The various quantum numbers are principal quantum number $ \left( n \right) $ , azimuthal quantum number $ \left( l \right) $ , magnetic quantum number $ \left( m \right) $ , spin quantum number $ \left( s \right) $ .

Complete Step By Step Answer:
In the question, it is given p-orbital with $ n = 5 $ and $ m = 1 $ . We have to find the number of electrons in p-orbital.
Principal quantum number $ \left( n \right) $ tells about the principal energy level or shell to which the electron belongs. We have $ n = 5 $ . Thus, the electrons belong to $ {5^{th}} $ shell.
Magnetic quantum number $ \left( m \right) $ gives information about the orbitals present in the subshell. We are given $ m = 1 $ .
Thus the orbital is $ 5p $ . Now we have to determine the number of electrons in this orbital.
Pauli exclusion principle states that:
An orbital can have a maximum of two electrons and these must have opposite spins.
 So, according to the Pauli exclusion principle each orbital of a subshell can have a maximum of two electrons only.
Thus, the number of electrons in p-orbital with $ n = 5 $ and $ m = 1 $ that is 5p orbital is 2.
The correct answer is $ B) $ that is 2 electrons.

Note :
 It should be carefully noted that the maximum number of electrons in any orbital is always $ 2 $ but the maximum number of electrons that can be accommodated in any subshell or shell can be calculated. The Pauli exclusion principle also states that no two electrons in an atom can have the same set of four quantum numbers.