Energia e Quantità di moto Relativistiche N° 4

m_{0} c^{2} = \frac{m_{0} c^{2}}{\sqrt{1 - β^{2}}} - m_{0} c^{2} \to 2 m_{0} c^{2} = \frac{m_{0} c^{2}}{\sqrt{1 - β^{2}}} \to \sqrt{1 - β^{2}} = \frac{1}{2} \to β^{2} = 1 - \frac{1}{4} \to β = \sqrt{\frac{3}{4}} = \frac{\sqrt{3}}{2}

Se l'energia cinetica eguaglia l'energia a riposo: $m_{0} c^{2} = \frac{m_{0} c^{2}}{\sqrt{1 - β^{2}}} - m_{0} c^{2} \to 2 m_{0} c^{2} = \frac{m_{0} c^{2}}{\sqrt{1 - β^{2}}} \to \sqrt{1 - β^{2}} = \frac{1}{2} \to β^{2} = 1 - \frac{1}{4} \to β = \sqrt{\frac{3}{4}} = \frac{\sqrt{3}}{2}$