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Re: [Phys-L] playing for keeps

Ah, yes! Thanks to all who posted hints. I didn't immediately think of this method (although yes, I do remember Avogadro's constant, at least the first four digits of it), since I generally think of this as as a _unit_conversion_ and point out to my classes that the atomic weight information on the periodic table wall chart can be read with two different units: grams/mol or u/atom.

So

gram / mol = u/atom, and we can rearrange to get

u = gram (atom/mol) = gram (1 atom)/(N_A atom) = (1/N_A )gram, so the conversion constant between u and gram is the inverse of Avogadro's constant.

Actually, I use 1 u = 1.661 x 10^-27 kg at least as much as 6.022 x 10^23 g/mol, so it's been years since I used either to find the other.

And yes, 1.66 x 10^-27 kg can serve as a first approximation for mass of the hydrogen atom, the proton or the neutron. Since nuclear was my secondary emphasis in grad school, I still remember 1 u as 931.5 MeV, m_p as 938.3 MeV and m_n as 939.6 MeV (over c^2). If I need more digits I look them up.

With all this discussion on this thread, I'm very surprised no-one has yet used the expression "Fermi estimate". We teach reasonable guessing as part of each beginning physics class: introductory physics, general physics (algebra/trig-based) and university physics (calculus-based). I also tell my students that they need to be able to " figure out whether their calculator has lied to them" (wrong button pushed, or otherwise). Multiple methods of estimating the same quantity are an important check.

KC

-----Original Message-----
From: Phys-l [mailto:phys-l-bounces@phys-l.org] On Behalf Of richard lindgren
Sent: Saturday, 29 June 2013 3:19 PM
To: Phys-L@Phys-L.org
Subject: Re: [Phys-L] playing for keeps

Good call,
Took me years after grad school when teaching to realize this.
I wonder how many others still don't get it.
Richard Lindgren






On Jun 29, 2013, at 9:54 AM, Richard Taylor <rtaylor.physics@tx.rr.com> wrote:

I imagine he figures everybody knows Avagadro's number. The mass of a proton is the reciprocal.

------
Richard Taylor

Sent from my iPad

On Jun 29, 2013, at 8:00 AM, brian whatcott <betwys1@sbcglobal.net> wrote:

On 6/29/2013 7:21 AM, Ken Caviness wrote:
Question for JSD! What method do you use to almost immediately figure out the mass of the proton within 1% accuracy, so you haven't had to take the time and trouble to memorize it? Tantalizing hint (can be done in less time than it takes to ask the question), but I'm drawing a blank -- unless you remember other things more easily, and find m_p from them? (For example, the m_p/m_e ratio, or the nuclear magneton, or ....)
/snip/


I am undoubtedly missing the thrust of Ken's question, but recalling Mp/Me is rather large, I can use the hydrogen mass as a good proxy for Mp.

Brian Whatcott Altus OK
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