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In physics, conservation of momentum is a fundamental principle. It states that the total momentum in a closed system remains constant if no external forces act on it. When a photon is emitted from an atom, the system (atom plus photon) must conserve its momentum.
The photon moves in one direction, while the atom recoils in the opposite direction to balance the momentum.
In this context, the momentum of the photon is equal and opposite to the recoil momentum of the atom. The momentum conservation equation can be expressed as:

• The momentum of the photon: \( p_{photon} = \frac{E}{c} \)
• The momentum of the atom: \( p_{atom} = mv \)

Here, \(E\) is the energy of the photon, \(c\) is the speed of light, \(m\) is the mass of the atom, and \(v\) is the recoil speed of the atom. This equation helps us understand how changes in one part of the system affect the other.

Recoil speed refers to the speed at which an atom moves in the opposite direction after emitting a photon. Since momentum must be conserved, the energy from photon emission affects the atom's speed.
To find the recoil speed, we use the conservation of momentum concept. Given the photon's momentum is \( \frac{E}{c} \) and must match that of the atom, we write:

• Momentum equation: \( mv = \frac{E}{c} \)
• Solving for \(v\): \( v = \frac{E}{mc} \)

This equation shows us how the energy of the photon and the mass of the atom determine the recoil speed.
It's crucial to handle calculations carefully, especially when involving such small energies and large masses.

The energy of a photon is a key quantity tied to its momentum and overall physics interactions. When a photon is emitted during an atomic transition, it carries away energy that can be calculated using its frequency or wavelength.
The relation between energy and momentum for a photon is:

• Photon energy: \( E = p c \)
• Photon momentum: \( p = \frac{E}{c} \)

Here, \(E\) is the energy, \(p\) is the momentum, and \(c\) is the speed of light. The energy is typically much smaller compared to the atom's rest energy.
This is due to the fact that the photon is massless, yet it carries energy and momentum as described by these equations.

Non-relativistic motion refers to the scenario where speeds involved are much lower than the speed of light. In such cases, classical Newtonian mechanics applies without the need to account for relativistic effects.
For the atom recoil scenario, since energy \(E\) is significantly less than \(mc^2\), the recoil speed \(v\) is much less than \(c\).
This condition allows us to safely ignore relativistic adjustments. The relation can be expressed as:

• Speed relationship: \( v = \frac{E}{mc} \)
• Non-relativistic condition: \( \frac{E}{mc^2} \ll 1 \)

This ensures our calculations remain valid without overly complex equations.
Understanding this concept helps streamline approaches to such physcial phenomena where very high speeds are not involved.