Question

The principal quantum number increases, the difference of energy between consecutive energy level:
(A) Decreases
(B) Increases
(C) Remaining the same
(D) Sometimes increases and sometimes decreases

Answer 1

Hint :Principal quantum number tells us about the principal energy level or shell to which the electron belongs and is represented by n(where n can be any integral value except zero).

Complete Step By Step Answer:
We get the complete information about the electrons present in an atom about their location, energy, type of orbital occupied, space and orientation with the help of quantum numbers.
The three types of quantum numbers are principal, azimuthal and magnetic and the principal quantum number tells the principal energy level or shell to which the electron belongs.
The value of n can be $ 1,2,3,4... $ and so on. The different principal energy shells are K, L, M, N, O… and so on.
The difference in energy = $ -\dfrac{{{Z}^{2}}R}{{{n}^{2}}} $
where,
Z is atomic number of the atom
and n is the principal quantum number.
Here, the negative sign indicates the spin of the electron.
Therefore, we can deduce that principal quantum number (n) and energy difference have inverse relation. This means that as the value of the principal quantum number that is n increases the difference between energy of consecutive energy levels decreases.
Hence, the correct option is A.

Note :
This relation directly shows us and gave us a rough idea as to how both the quantities are related. But to get the exact idea if we need to find exactly how they both will matter we need to take care of the square powered n.