As the principal quantum number increases, the energy difference between successive energy levels decreases. Why?

Question

abb0t · Answer

As n increases for a given atom, so does the average distance of an electron from the nucleus

anonymous · Answer

but how does that explain why the energy difference between n=1 and n=2 would be greater than n=4 and n=5?

anitaasks · Answer

The energy of an orbital is given by the formula, energy of orbital= -2.18E-18(Z^2/n^2) 
so as n increases, the energy is smaller

aaronq · Answer

The principle quantum number relates to the distance of an electron to the nucleus. if you model an atom with the nucleus (protons) as a point charge, you can see that electric field of the atom decays with as an inverse square of the radius ($E=\dfrac{1}{r^2}$).

To illustrate how the energy difference between successive energy levels decreases, compare the differences of two distances from the nucleus, 0.1 and 0.2 vs 0.4 and 0.5

$\dfrac{1}{(0.1)^2}=100$       $\dfrac{1}{(0.2)^2}=25$        difference of 75

$\dfrac{1}{(0.4)^2}=6.25$      $\dfrac{1}{(0.5)^2}=4$          difference of 2.25