How many maxima would you expect to find in the radial probability function for the 4s orbital of the hydrogen atom?

Here we have to predict the number of maxima will be there in the radial probability function of 4s orbital of the hydrogen atom.

There will be four (4) maxima in the radial probability function for the 4s orbital of the hydrogen atom.

We know that the probability of finding an electron at some point is proportional to the square of the Hamiltonian function (Ψ). The Ψ² is equivalent to the 4Πr²Rdr. Which is actually the probability that an electron will be found in this volume R²dV or 4Πr²Rdr. The r is the radius of the orbital.

Now when r = 0, R is not zero it has a maxima if we draw r vs radial probability curve for an electron. The r maxima of the curve is the 1st Bohr orbital for the hydrogen atom.

As the r increases the R approaches to zero exponentially and also 4Πr²Rdr, which relates to the size of the orbit. We observe as we move from 1s→2s→3s→4s, the maximum density of electron occurs at larger distance.

As for 4s the corresponding orbit is four so we will get four (4) maxima in the radial probability which will be apart from the nucleus of the hydrogen atom.