What are the challenges in calculating the Bohr radius?

[robertjford80]

Homework Statement

the equation for the bohr radius is

4pi (permitivity of free space) * (reduced Planck constant)/
(elementrary charge)²(mass of an electron)

The Attempt at a Solution

let's just just focus on orders of magnitude:

(10^-12 * 10^-34)/(((10^-19)^2)*(10^-31)

That's 10^-46/10^-69 which works out to about 10^13 way off of the 10^-11

 

[cepheid]

There are a few problems here:

1. It's supposed to be the reduced Planck constant squared. This makes a huge difference.

2. When doing an order of magnitude estimate, you can't just completely ignore the numbers that multiply the powers of ten. You can imagine that their product can add on another couple of orders of magnitude. Instead, try rounding them to one sig fig. You also certainly can't ignore the factor of 4pi! That's like 13...another order of magnitude right there. So in the end, a better estimate would be something like this:

4*pi *(9e-12)(1e-34)^2/(2e-19)^2*(10e-31)

9e-12 is almost 1e-11, illustrating why it's perilous to ignore the coefficients.