New solution

astrosander edited
revision #13989 newer →
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+### Statement
+
+$14.5.6.$ [Insert the problem statement]
+
+### Solution
+
+### Problem
+
+**14.5.6.** A stationary atom of mass \( M \) absorbs a photon of mass \( m \). Determine the mass and momentum of the atom after the photon is absorbed.
+
+### Solution
+
+A photon has momentum \( p_{\gamma} = mc \), and after absorption, this momentum must be conserved. Let the atom move with momentum \( p \) after absorbing the photon, then:
+
+$$
+p = mc
+$$
+
+The initial energy of the system is the rest energy of the atom plus the energy of the photon:
+
+$$
+E_{\text{initial}} = Mc^2 + mc^2
+$$
+
+After absorption, the atom will have a new mass \( M_1 \) and kinetic energy:
+
+$$
+E_{\text{final}} = M_1 c^2
+$$
+
+Since total energy must be conserved:
+
+$$
+Mc^2 + mc^2 = M_1 c^2
+$$
+
+Solving for the new mass of the atom:
+
+$$
+M_1 = M + m
+$$
+
+#### Answer
+
+\[
+M_1 = M + m \\
+p = mc
+\]
+
+#### Answer
+
+[Insert a concise answer or boxed result]