Mass of Helium

[Gareth56]

Whist reading a book on how nuclear fusion takes place in stars I noted that 4 hydrogen atoms are converted 1 Helium atom with the resulting mass difference being converted into energy via E = mc^2.

 

In their calculation (ignoring the mass of the electron) they gave the mass of 4 hydrogen atoms as 6.692 x 10^-27kg which I concur with as 1 proton = 1.673 x 10^-27kg therefore 4 protons = 4 x 1.673 x 10^-27kg = 6.692 x 10^-27kg

 

But it's the mass of the He atom that I'm unsure about. It states in the book that the mass of the He atom = 6.645 x 10^-27kg. However I understand a (normal) He atom (again ignoring the mass of the electrons) to comprise of 2 protons & 2 neutrons making a mass calculation of:-

 

(2 x 1.673 x 10^-27kg) + (2 x 1.675 x 10^-27kg) = 6.696 x 10^-27kg

 

This is again shown by the RAM of He to be 4.0026 which again gives the mass of the He atom as 1.673 x 10^-27kg x 4.0026 = 6.696 x 10^-27kg.

 

 

Is the mass of He given in the book wrong?

 

Thanks.

[swansont]

The mass of He-4 is going to be less than the mass of the constituents, because the system is bound together, and energy must be released for this to happen. In the case of He-4, this is about 28.3 MeV, which has a mass equivalent of 0.0304 atomic mass units

 

1.673 x 10^-27kg is not the conversion factor between kg and atomic mass units; the proton (or Hydrogen atom) does not have a mass of exactly 1 amu. The conversion factor is the inverse of Avogadro's number (expressed in kg/mole) which you should be able to deduce from the definition of the atomic mass unit. If you convert 4.0026 amu, you get

 

[math]\frac{4.0026}{6.022 x 10^{26}} = 6.647 x 10^{-27}kg[/math]

[Gareth56]

Thanks for the clarification but I'm still a tad confused because the book states the following:-

 

"To see how much mass is consumed, we compare the combined mass of four hydrogen atoms (the ingredients) to the mass of one helium atom (the product)

 

 

4 hydrogen atoms = 6.692 x 10^-27kg

- 1 Helium atom = 6.645 x 10^-27kg

Mass lost = 0.048 x 10^-27 kg

 

 

What I don't follow is that when determining the mass of the 4 hydrogen atoms I assume you just multiply the mass of a proton i.e. 1.673 x 10^-27kg by 4 to get 6.692 x 10^-27kg, so why can't you just add up the masses of the two protons and the two neutrons which make up the nucleus of a Helium atom to get the mass of the Helium atom (ignoring the masses of the electrons).

 

Is it a case that the book doesn't go into the detail of why the mass of the Helium atom is less than what you would expect by just adding up the masses of the nucleons?

 

Thanks

[insane_alien]

the bound system has less energy than the free protons and neutrons. this means it weighs less.

 

you have to account for the energy of bound systems when you're dealling with atomic nuclei as it forms a significant proportion of the mass.

[Gareth56]

So not a case of simply adding the masses of the individual nucleons up!!

 

Many thanks