Electron Collides Elastically with Stationary Hydrogen Atom
Elastic Collision of Electrons with Hydrogen Atoms at Stationary
There are electrons in elastic collision with hydrogen atoms at rest.
Elastic colliders have momentum and kinetic energy conserved. Let the mass of the electron be\ (m_ {e}\), the initial velocity is\ (v_ {0}\), the speed of the electron after the collision is\ (v_ {1}\), the mass of the hydrogen atom is\ (m_ {H}\), and the speed of the hydrogen atom after the collision is\ (v_ {2}\).
According to the law of conservation of momentum, there is\ (m_ {e} v_ {0} = m_ {e} v_ {1} + m_ {H} v_ {2 }\) ①;
According to the law of conservation of kinetic energy, we can get\ (\ frac {1} {2} m_ {e} v_ {0} ^ {2} =\ frac {1} {2} m_ {e} v_ {1} ^ {2} +\ frac {1} {2} m_ {H} v_ {2} ^ {2}\) ②.
From the formula ① we get\ (m_ {e} (v_ {0} - v_ {1}) = m_ {H} v_ {2 }\) ③;
The deformation of the formula ② gives\ (m_ {e} (v_ {0} ^ {2} - v_ {1} ^ {2}) = m_ {H} v_ {2} ^ {2 }\) ④;
Substitute ③ into ④, that is,\ (m_ {e} (v_ {0} + v_ {1}) (v_ {0} - v_ {1}) = m_ {H} v_ {2}\ cdot v_ {2}\), Since\ (m_ {e} (v_ {0} - v_ {1}) = m_ {H} v_ {2}\),\ (v_ {0} + v_ {1} = v_ {2}\) ⑤.
Substitute ⑤ into ① to get\ (m_ {e} v_ {0} = m_ {e} v_ {1} + m_ {H} (v_ {0} + v_ {1}) \), and organize to get\ (v_ {1} =\ frac {m_ {e} - m_ {H}} {m_ {e} + m_ {H}} v_ {0 }\) ⑥;
Substitute ⑥ into ⑤ to get\ (v_ {2} =\ frac {2m_ {e}} {m_ {e} + m_ {H}} v_ {0}\) 0006.
The velocity of the electron and the hydrogen atom after the collision can be known from (6) 0006. The relationship between the velocities of the two is determined by the masses of the electron and the hydrogen atom and the initial velocity of the electron.
There are electrons in elastic collision with hydrogen atoms at rest.
Elastic colliders have momentum and kinetic energy conserved. Let the mass of the electron be\ (m_ {e}\), the initial velocity is\ (v_ {0}\), the speed of the electron after the collision is\ (v_ {1}\), the mass of the hydrogen atom is\ (m_ {H}\), and the speed of the hydrogen atom after the collision is\ (v_ {2}\).
According to the law of conservation of momentum, there is\ (m_ {e} v_ {0} = m_ {e} v_ {1} + m_ {H} v_ {2 }\) ①;
According to the law of conservation of kinetic energy, we can get\ (\ frac {1} {2} m_ {e} v_ {0} ^ {2} =\ frac {1} {2} m_ {e} v_ {1} ^ {2} +\ frac {1} {2} m_ {H} v_ {2} ^ {2}\) ②.
From the formula ① we get\ (m_ {e} (v_ {0} - v_ {1}) = m_ {H} v_ {2 }\) ③;
The deformation of the formula ② gives\ (m_ {e} (v_ {0} ^ {2} - v_ {1} ^ {2}) = m_ {H} v_ {2} ^ {2 }\) ④;
Substitute ③ into ④, that is,\ (m_ {e} (v_ {0} + v_ {1}) (v_ {0} - v_ {1}) = m_ {H} v_ {2}\ cdot v_ {2}\), Since\ (m_ {e} (v_ {0} - v_ {1}) = m_ {H} v_ {2}\),\ (v_ {0} + v_ {1} = v_ {2}\) ⑤.
Substitute ⑤ into ① to get\ (m_ {e} v_ {0} = m_ {e} v_ {1} + m_ {H} (v_ {0} + v_ {1}) \), and organize to get\ (v_ {1} =\ frac {m_ {e} - m_ {H}} {m_ {e} + m_ {H}} v_ {0 }\) ⑥;
Substitute ⑥ into ⑤ to get\ (v_ {2} =\ frac {2m_ {e}} {m_ {e} + m_ {H}} v_ {0}\) 0006.
The velocity of the electron and the hydrogen atom after the collision can be known from (6) 0006. The relationship between the velocities of the two is determined by the masses of the electron and the hydrogen atom and the initial velocity of the electron.

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