Calculating Mass Difference in H Atom from Proton & Electron

Click For Summary
SUMMARY

The discussion focuses on calculating the mass difference in a hydrogen atom formed from a proton and an electron, which initially are at rest and far apart. When these particles combine, they release 13.6 eV of energy, primarily as light. The key question is determining the mass difference between the hydrogen atom and the sum of the masses of the proton and electron, as well as calculating the fractional difference ΔM / (m_e + m_p). The relevant equation for this calculation is E = √((pc)² + (mc²)²), with the assumption that momentum p is zero.

PREREQUISITES
  • Understanding of mass-energy equivalence (E=mc²)
  • Familiarity with photon energy calculations
  • Basic knowledge of quantum mechanics principles
  • Proficiency in algebra and solving equations
NEXT STEPS
  • Study the concept of mass-energy equivalence in detail
  • Learn how to calculate energy released in atomic transitions
  • Explore the implications of binding energy in atomic physics
  • Investigate the relationship between mass and energy in particle physics
USEFUL FOR

Students in physics, particularly those studying atomic structure and energy interactions, as well as educators and anyone interested in the principles of mass-energy conversion in quantum mechanics.

knowLittle
Messages
307
Reaction score
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
 
Physics news on Phys.org
knowLittle said:

Homework Equations


E= √( (pc)^2 + (mc^()2)^2 )

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

Similar threads

  • · Replies 10 ·
Replies
10
Views
4K
  • · Replies 0 ·
Replies
0
Views
2K
  • · Replies 3 ·
Replies
3
Views
1K
Replies
9
Views
3K
  • · Replies 9 ·
Replies
9
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 1 ·
Replies
1
Views
3K
  • · Replies 26 ·
Replies
26
Views
5K
  • · Replies 10 ·
Replies
10
Views
19K