183_notes:rest_mass

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183_notes:rest_mass [2014/10/03 20:54] – [Neutron Decay] caballero183_notes:rest_mass [2021/05/06 20:02] (current) – [Example: Neutron Decay] stumptyl
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 ===== Change of Rest Mass Energy ===== ===== Change of Rest Mass Energy =====
  
-Until now, you have dealt with particles that do not change their identity. Changing the identity of a particle occurs when a [[http://en.wikipedia.org/wiki/Nuclear_fission|particle decays to another particle]] (or, typically, set of particles), or when [[http://en.wikipedia.org/wiki/Nuclear_fusion|two or more particles fuse together]]. In these notes, you will read about a new unit of energy (the [[http://en.wikipedia.org/wiki/Electronvolt|electron volt]]) and how to use energy to predict or explain particle decay. +Until now, you have dealt with particles that do not change their identity. Changing the identity of a particle occurs when a [[http://en.wikipedia.org/wiki/Nuclear_fission|particle decays to another particle]] (or, typically, set of particles), or when [[http://en.wikipedia.org/wiki/Nuclear_fusion|two or more particles fuse together]]. **In these notes, you will read about a new unit of energy (the [[http://en.wikipedia.org/wiki/Electronvolt|electron volt]]) and how to use energy to predict or explain particle decay. 
 +**
 ==== The Electron Volt ==== ==== The Electron Volt ====
  
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 ^ Particle        ^ Rest Mass Energy (MeV) ^ ^ Particle        ^ Rest Mass Energy (MeV) ^
 +| Neutrino, $\nu$ | $\approx$ 0 MeV        |
 | Electron, $e^-$ | 0.511 MeV              | | Electron, $e^-$ | 0.511 MeV              |
 | Proton,   $p^+$ | 938.8 MeV              | | Proton,   $p^+$ | 938.8 MeV              |
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-==== Neutron Decay ====+==== Example: Neutron Decay ====
  
 +[{{ 183_notes:week7_decay.png?400|A neutron will spontaneously decay into a proton, electron, and an anti-neutrino.}}]
 As an example of the change of particle identity, consider [[http://en.wikipedia.org/wiki/Neutron#Free_neutron_decay|decay of a neutron]] where a neutron spontaneously decays into a proton, an electron, and an [[http://en.wikipedia.org/wiki/Neutrino|anti-neutrino]]. A neutron is at rest and spontaneously decays, let's determine the kinetic energy available for the decay products after the decay. As an example of the change of particle identity, consider [[http://en.wikipedia.org/wiki/Neutron#Free_neutron_decay|decay of a neutron]] where a neutron spontaneously decays into a proton, an electron, and an [[http://en.wikipedia.org/wiki/Neutrino|anti-neutrino]]. A neutron is at rest and spontaneously decays, let's determine the kinetic energy available for the decay products after the decay.
  
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    - Surroundings: nothing much    - Surroundings: nothing much
  
-So you can apply the energy principle to this problem.+So you can apply the [[183_notes:define_energy|energy principle]] to this problem to find the sum of all the kinetic energies.
  
 $$E_{sys,f} = E_{sys,i} + W$$ $$E_{sys,f} = E_{sys,i} + W$$
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 The system energies consist of the sum of the rest mass energies and the kinetic energies of the particles. The system energies consist of the sum of the rest mass energies and the kinetic energies of the particles.
  
-$$(m_pc^2 +K_p) + (m_ec^2 + K_e) + K_{\bar{\nu}}$$+$$(m_pc^2 +K_p) + (m_ec^2 + K_e) + K_{\bar{\nu}} = (m_nc^2 + K_n) + W $$ 
 +$$(m_pc^2 +K_p) + (m_ec^2 + K_e) + K_{\bar{\nu}} = (m_nc^2 + 0) + 0 $$ 
 +$$(m_pc^2 + m_ec^2) +K_p + K_e + K_{\bar{\nu}} = m_nc^2 $$ 
 +$$(m_pc^2 + m_ec^2) + (K_p + K_e + K_{\bar{\nu}}) = m_nc^2 $$ 
 +$$K_p + K_e + K_{\bar{\nu}} = m_nc^2  - (m_pc^2 + m_ec^2)$$ 
 +$$K_p + K_e + K_{\bar{\nu}} = 939.6 MeV  - (938.3 MeV + 0.511 MeV)$$ 
 +$$K_p + K_e + K_{\bar{\nu}} = 0.8MeV$$ 
 + 
 +This energy is available to the products for their motion. This decay must also [[183_notes:collisions|conserve momentum]], so the decay products cannot all move in the same direction after the decay. There is no external force acting on the neutron during the decay, so that the change in momentum of the system must be zero.
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