This preview shows pages 1–2. Sign up to view the full content.
Dimensional Analysis for HydrogenLike Atoms
In this example we are considering atoms with a heavy nuclear charge of +
Ze
(
Z
is the number
of protons) with total mass
M
nucl
, and a single electron with charge

e
and mass
m
e
±
M
nucl
.
We’ll apply the procedure for doing systematic dimensional analysis that was presented in an
earlier handout to ﬁnd out about the characteristic size of the radius and energy.
General Procedure
1. Determine the relevant quantities from
physics
considerations, often based on the
equation(s) that determine how the system behaves.
2. Determine the fundamental units (e.g., [
M
], [
L
], [
T
]) of each quantity.
3. Postulate an equation relating the quantities, with unknown exponents (
a
,
b
, ...).
4. Substitute units.
5. Equate exponents of [
M
], [
L
], [
T
] and solve the resulting equations simultaneously.
6. Check your results by plugging back into the equations. Check whether the physics makes
sense.
Ok, now we apply the steps .
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview. Sign up
to
access the rest of the document.
 Spring '11
 Furnstahl
 Charge, Mass, Quantum Physics

Click to edit the document details