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https://texercises.com/exercise/alpha-particle-2/
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The following quantities appear in the problem: Masse \(m\) / Energie \(E\) / Geschwindigkeit \(v\) / Lorentz-Faktor \(\gamma\) /
The following formulas must be used to solve the exercise: \(E_k = (\gamma-1)mc^2 \quad \) \(\gamma = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}} \quad \)
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Exercise:
Calculate the velocity of an alpha particle with a kinetic energy of EkO.

Solution:
The Lorentz factor is gamma +fracsscEkinE_ fracE_ + sscEkinE_ It follows for the velocity beta sqrt-fracgamma^ beF sqrt-fracEr^Er+Ek^ resultbeP The classical calculation yields a value of v_textrmcl sqrtfrac sscEkinm vcF sqrtfrac times EkErtimes c vcP In this example the classical calculation is only slighty higher than the relativistic one. For higher velocities the deviations become much more significant.
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Exercise:
Calculate the velocity of an alpha particle with a kinetic energy of EkO.

Solution:
The Lorentz factor is gamma +fracsscEkinE_ fracE_ + sscEkinE_ It follows for the velocity beta sqrt-fracgamma^ beF sqrt-fracEr^Er+Ek^ resultbeP The classical calculation yields a value of v_textrmcl sqrtfrac sscEkinm vcF sqrtfrac times EkErtimes c vcP In this example the classical calculation is only slighty higher than the relativistic one. For higher velocities the deviations become much more significant.
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special relativity
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kinetic energy, lorentz factor, rest energy
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(2, default)
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ENG (English)
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Calculative / Quantity
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