The hydrogen atoms orbitals are the "wavefunction" portion of the quantum mechanical solution to the hydrogen atom. The wavefunctions tell us about the probability of finding the electron at a certain point in space. Thus the orbitals offer us a picture of the electron in a hydrogen atom. However, this picture is not a simple one. First of all, the electron is spread out over space. We cannot pin-point its location. If this seems odd (even impossible), it should. Electrons are inherently quantum mechanical and behave differently than everything we encounter in our everyday life. As we build up from the hydrogen atom to multi-electron atom to bonding and molecules we will make extensive use of the wavefunctions that we first find for hydrogen. As such it is useful to become familiar with their shapes.
There are two key features for an orbital. The distribution of the electron away from the nucleus. This is known as the radial distribution. The other is the "shape" of the orbital and is the angular distribution. The radial distribution is mostly dependent on the principle quantum number n. The angular distribution depends on \( \ell\) and \(m_{\ell}\).
s orbitals are wavefunctions with \(\ell\) = 0. They have an angular distribution that is uniform at every angle. That means they are spheres.
This link shows some picture of this distribution. In fact, this link is to the orbitron page that contains lots of great plots of these orbitals.The radial probability distribution (the probability of finding the electron at a particular radius) starts at zero at the nucleus, increases, and then decays away to zero as the radius increases. A radial distribution plot for the 1s orbital (n=1, \(\ell\) =0) can be found here .
Higher energy s orbitals such as 3s (n=3, \(\ell\) =0) have "nodes" at particular distances. These are distances at which the electron has zero probability. This is a consequence of the quantum mechanical nature of the electron. It appears to have wave-like properties. As such there are regions in space where the amplitude (probability) is zero. You can see this clearly in a radial distribution function for the 3s . There is a node at two distances away from the nucleus (r = 0). Note: the probability is zero at the nucleus as well but this is the result of the finitely small volume at r=0 not a radial node.
p orbitals are wavefunctions with \(\ell\) = 1. They have an angular distribution that is not uniform at every angle. They have a shape that is best described as a "dumbbell". A picture of this distribution can be found here for a 2p
p orbitals have one angular node (one angle at which the probability of electron is always zero. The radial probability distribution (the probability of finding the electron at a particular radius) for a 2p, looks nearly identical to a 1s. What is different? Mostly the angular distribution. A plot for the 2p orbital (n=2, \(\ell\) =1) can be found here .
Higher energy p orbitals such as 3p (n=3, \(\ell\) =1) have the same angular distribution, but now the start to be "nodes" at particular distances in the radial distribution. You can see this clearly in a radial distribution function for the 3p . There is a node at one distance away from the nucleus (r = 0). Note: the probability is zero at the nucleus as well but this is the result of the infinitely small volume at r=0, not a radial node.
There are three different p orbitals that are nearly identical for the three different \( m_{\ell}\) values (-1,0,+1). These different orbitals essentially have different orientations.
d orbitals are wavefunctions with \(\ell\) = 2. They have an even more complex angular distribution than the p orbitals. For most of them it is a "clover leaf" distribution (something like 2 dumbbells in a plane). dorbitals have two angular nodes (two angles at which the probability of electron is always zero.
There are five different d orbitals that are nearly identical (n=2, \(\ell\) =1) for the five different \( m_{\ell}\) values (-2,-1,0,+1,+2). These different orbitals essentially have different orientations. There is one that is a little different than the others (this is the \(m_{\ell}\)=0). The shapes of the d orbitals can be seen here for a 3d
As n increases there are ever larger available \(\ell\) numbers. These give even more complex angular distributions with more angular nodes. After the d orbitals \(\ell\)=2, come the f \(\ell\)=3, then g \(\ell\)=4, then h\(\ell\)=5, ....