Answer:
the energy difference between adjacent levels decreases as the quantum number increases
Explanation:
The energy levels of the hydrogen atom are given by the following formula:
[tex]E=-E_0 \frac{1}{n^2}[/tex]
where
[tex]E_0 = 13.6 eV[/tex] is a constant
n is the level number
We can write therefore the energy difference between adjacent levels as
[tex]\Delta E=-13.6 eV (\frac{1}{n^2}-\frac{1}{(n+1)^2})[/tex]
We see that this difference decreases as the level number (n) increases. For example, the difference between the levels n=1 and n=2 is
[tex]\Delta E=-13.6 eV(\frac{1}{1^2}-\frac{1}{2^2})=-13.6 eV(1-\frac{1}{4})=-13.6 eV(\frac{3}{4})=-10.2 eV[/tex]
While the difference between the levels n=2 and n=3 is
[tex]\Delta E=-13.6 eV(\frac{1}{2^2}-\frac{1}{3^2})=-13.6 eV(\frac{1}{4}-\frac{1}{9})=-13.6 eV(\frac{5}{36})=-1.9 eV[/tex]
And so on.
So, the energy difference between adjacent levels decreases as the quantum number increases.
