# What is the Energy of a Photon Released in Atom Decay with a Change in Mass?

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In summary, using the laws of energy and momentum, the energy of a photon released during the decay of an atom from an excited state to the ground state can be determined. However, this calculation may be more complex due to the atom's motion and the resulting redshift of the photon's energy.
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## Homework Statement

An atom of mass M decays from an excited state to the ground state with a change in mass of ΔM<<M. In the decay process, the atom releases a photon. Use the laws of energy and momentum to determine the energy of the photon, assuming the atom decays from rest.

## Homework Equations

The 4-momenta of the atom before the emission:

P=(Mc2,0,0,0)

After the emission:

P=(M-ΔM)c2, -pxc,0,0)

And the photon:

E=(M-ΔM)c2

p = hf

My main concern here is that this seems too straightforward. The book labels this problem as a challenging one. I think I'm missing a subtlety in the problem.

Found it. The energy of the photon isn't delta(m)c^2 as the atom is moving. So in the atom's frame, the photon is redshifted. The energy of the photon (which is hf in a rest frame) is now hf', where f' is the shifted frequency due to the transverse relativistic doppler effect.

## 1. What is the process of atom decay to ground state?

The process of atom decay to ground state is known as spontaneous emission, in which an atom in an excited state releases energy in the form of a photon and transitions to a lower energy level, or the ground state.

## 2. How does an atom reach an excited state?

An atom can reach an excited state through various methods, such as absorbing energy from an external source or colliding with other particles.

## 3. What is the significance of an atom decaying to ground state?

The decay of an atom to ground state is important because it allows for the release of excess energy, which can be harnessed for various applications such as in lasers or medical imaging.

## 4. Can atoms decay to ground state multiple times?

Yes, atoms can decay to ground state multiple times if they are continuously excited or if they are in a system where they can repeatedly absorb and release energy.

## 5. Is the process of atom decay to ground state predictable?

The process of atom decay to ground state is unpredictable on an individual atom level, as it is a random process. However, on a large scale, the overall decay rate can be predicted and measured.

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