Answer to Question #120190 in Mechanics | Relativity for Ansa

Question #120190
What will be energy of proton if it is moving with 97% speed of light?
1
Expert's answer
2020-06-04T10:05:24-0400

Put that "\\alpha=0.97=v\/c." Then the energy of such a photon will be


"E=\\sqrt{p^2c^2+(m_0c^2)^2}=\\sqrt{\\frac{m_0^2\\alpha^2c^4}{1-\\alpha^2}+(m_0c^2)^2}=\\\\\\space\\\\\n=\\frac{m_0c^2}{\\sqrt{1-\\alpha^2}}=\\frac{1.673\\cdot10^{-27}(3\\cdot10^8)^2}{\\sqrt{1-0.97^2}}=1.671\\cdot10^{-17}\\text{ J},"

or 104.3 eV.


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