Calculating Mass Difference in H Atom from Proton & Electron

In summary, the formation of a hydrogen atom from an electron and proton results in a release of 13.6 eV of energy, mainly in the form of light. The mass of a hydrogen atom differs from the sum of the masses of the electron and proton by an amount ΔM, and the fractional difference is given by ΔM / (m_e + m_p). To calculate this, the equation E= √( (pc)^2 + (mc^()2)^2 ) can be used, assuming the momentum (p) is 0.
  • #1
knowLittle
312
3

Homework Statement



If an electron and proton (both initially at rest and
far apart) come together to form a hydrogen atom,
13.6 eV of energy is released (mostly as light). By
how much does the mass of an H atom differ from the
sum of the electron and proton masses? What is the
fractional difference ΔM / (m_e + m_p) ?


Homework Equations


E= √( (pc)^2 + (mc^()2)^2 )

E of photon= 13.6 eV

The Attempt at a Solution



Any help on how to proceed?
Can I say that energies of rest masses of proton and electron - 13.6 eV = Energy in H?

Thanks
 
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  • #2
knowLittle said:

Homework Equations


E= √( (pc)^2 + (mc^()2)^2 )

You can assume p=0. Then find the change in total energy!
 

1. What is the formula for calculating the mass difference in an H atom from proton and electron?

The formula for calculating the mass difference in an H atom is Δm = mp - me, where Δm is the mass difference, mp is the mass of a proton, and me is the mass of an electron.

2. How do you determine the mass of a proton and electron?

The mass of a proton and electron can be determined experimentally using a mass spectrometer or other specialized equipment. The current accepted values for the mass of a proton and electron are 1.007276 amu and 0.00054858 amu, respectively.

3. Why is it important to calculate the mass difference in an H atom?

The mass difference in an H atom is important because it helps us understand the fundamental structure of matter and the relationship between particles. It also allows us to make precise calculations and predictions in fields such as chemistry, physics, and astronomy.

4. How does the mass difference in an H atom affect its properties?

The mass difference in an H atom has a significant impact on its properties. For example, the mass difference between the proton and electron determines the atom's overall mass, which in turn affects its density, reactivity, and behavior in chemical reactions.

5. Can the mass difference in an H atom change?

The mass difference in an H atom is a constant value as long as the atom is in a stable state. However, in certain situations such as nuclear reactions, the mass difference can change due to the conversion of mass into energy or vice versa. This is described by Einstein's famous equation, E=mc².

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