# How an Increase in *r* Affects the Appearance of Hydrogen Wave Functions

In a hydrogen atom, the wave functions change as you change the orbital radius, *r*. So what do the hydrogen wave functions look like? Given that

looks like this:

Here are some other hydrogen wave functions:

Note that

behaves like *r** ^{l}* for small

*r*and therefore goes to zero. And for large

*r*,

decays exponentially to zero. So you’ve solved the problem of the wave function diverging as *r* becomes large — and all because of the quantization condition, which cut the expression for f(*r*) from an exponent to a polynomial of limited order. Not bad.

_{10}(

*r*).

You can see the radial wave function R_{10}(*r*) in the first figure. R_{20}(*r*) appears in the second figure. And you can see R_{21}(*r*) in the last figure.

_{20}(

*r*).

_{21}(

*r*).