### Question 2.3

Posted: **Fri Oct 14, 2016 5:29 pm**

by **Josh Clark 1J**

Consider the expression in Table 2.1 for hydrogen like atomic orbitals. (a) List the coordinates on which the wave functions of the following orbitals depend: (i) 2s, (ii) 2px (iii) 3dz2. (b) What fundamental constants determine the shapes of the orbitals? (c) What fundamental constants determine the extents of the orbital?

I'm confused about this question. Can someone explain what the coordinates (r, theta, etc.) mean as well as what the fundamental constants are?

### Re: Question 2.3 [ENDORSED]

Posted: **Mon Oct 24, 2016 12:27 pm**

by **Chem_Mod**

Please post a descriptive title in future posts so that students know the content of your question without having to click and read through the post.

Referring to Table 2.1 on page 35, we see that a 2s orbital only depends on the radius r. This is also intuitive because we know that s orbitals are like nearly hollow spheres of electron (probability) density that grow in radius with increasing n and thus need no other spherical coordinates to describe.

The 2p_{x} orbital will need to be described by θ and ϕ because we know p-orbitals are bi-lobed or "dumbbell" shaped orbitals. Thus we need contributions from both the radial and angular wavefunctions as seen in Table 2.1.

When we refer to Table 2.1 for the 3d_{z2} orbital, we see it will need a n=3, l=2 radial contribution and a l=2, m_{l}=z^{2} contribution. We can see the only coordinates needed in those expressions are r and θ.

Fundamental constants are values in science that describe the most fundamental physics of the natural world. From looking at the expressions used to derive the Schrödinger equation (page 32), we see such constants as e (fundamental charge), h (Planck's constant), m_{e} (mass of the electron), ε_{0} (vacuum permittivity). Such fundamental constants appear inside the back cover of you textbook. You will be seeing many of them quite often as you continue your studies.