# Find the binding energy of hydrogen

• warfreak131

## Homework Statement

Calculate the mass corresponding to the binding energy of an H atom. What fraction of the
mass of the atom is this?

BE=(mp+me-mH)c2

## The Attempt at a Solution

I couldn't figure this one out, so I searched for the answer online, and it's supposed to be 13.6 eV, but no matter what I do, none of my answers come even close to that.

I'm not clear what there is to be confused about. Take the mass of the hydrogen atom and you'll see it's less than the sum of the free masses of a proton and a neutron. The difference between the composite and its components is the mass-energy of the binding. Multiply by c^2 to get it in units of energy.

ok, maybe I am using incorrect numbers, i have the mass of a proton as 1.6726*10-27 g

and the mass of a neutron is 1.6749*10-27 g. What exactly is the mass of a hydrogen atom?

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okay, according to wikipedia, the "standard atomic mass" of hydrogen is 1.67492577 × 10-24 grams.

Hydrogen has 1 proton, no neutrons, and 1 electron. The book only says hydrogen atom, not deuterium or tritium, so i have to assume it means no neutrons.

This means that BE=(mp+me-mH)c2

BE=(1.6726*10-24 g + 9.1093*10-28 g - 1.6749*10-24 g)(3*1010)2

This equals -1.25016*10-6 ergs, or -780 288 eV

anyone? anyone? what am i doing wrong here!?

I noticed some discrepancies between masses from various online sources, even page to page on wikipedia. The latest best values (as of 2006) are at:

http://physics.nist.gov/cuu/index.html" [Broken]

m_p = 1.672 621 637(83) x 10-27 kg
m_e =9.109 382 15(45) x 10-31 kg

the atomic mass unit: u=1.660 538 782(83) x 10-27 kg

all except for the hydrogen mass. Here you have to be very careful as some values are averaged over percentage of naturally occurring isotopes. So with hydrogen the standard number is a bit high due to the small percentage of deuterium in common hydrogen.

Here's the atomic mass of 1H (Protium) of:
m_H=1.0078250321(4)u
(from the 2001-2002 CRC Handbook of Chemistry and Physics 82nd Ed., p. 1-15.)

That comes to:
m_H= 938.782999(23) MeV

EDIT: or 1.673 532 551(84) x 10^-27 kg. Compare with the value you have!

It is simplest to convert to MeV and look up the mass energy equivalents of m_e and m_p.

But you need to carry through the error bars in each quantity as well as in the conversion factors. I worked it out and got a value with error larger than the value so it gives at best an order of magnitude boundary for the binding energy.

By the way. The physics.nist.gov website has an energy unit calculator
http://physics.nist.gov/cuu/Constants/energy.html" [Broken]
which includes the error factors, very very handy!

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thank you, i appreciate it, ill be sure to check those links out.

Followup...

I found where to get the atomic mass data:
http://physics.nist.gov/PhysRefData/Elements/index.html" [Broken]

Click on the element in the periodic table then hit the [isotopic] link under Nuclear Physics Data.

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Followup...

I found where to get the atomic mass data:
http://physics.nist.gov/PhysRefData/Elements/index.html" [Broken]

Click on the element in the periodic table then hit the [isotopic] link under Nuclear Physics Data.

thats a really good site, thank you

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okay, according to wikipedia, the "standard atomic mass" of hydrogen is 1.67492577 × 10-24 grams.

"Standard atomic mass" takes all the naturally occurring isotopes, and their relative abundance into consideration. So that's not the number you want to use here.

Instead, try the "Isotope mass" of Hydrogen 1.
http://en.wikipedia.org/wiki/Hydrogen-1