Answer to Question #285674 in Mechanics | Relativity for Amos baite

Question #285674

What is the velocity o π- meson whose proper means life time is 2.5× 10⅞ second

1
Expert's answer
2022-01-10T14:23:21-0500

We know that

τ=τ0(1v2c2)\tau=\frac{\tau_0}{\sqrt{(1-\frac{v^2}{c^2}})}

τ=τ0×2.5×1078\tau=\tau_0\times2.5\times10^{\frac{7}{8}}

τ0×2.5×1078=τ0(1v2c2)\tau_0\times2.5\times10^{\frac{7}{8}}=\frac{\tau_0}{\sqrt{(1-\frac{v^2}{c^2}})}

Both sides take square

6.25×1074=11v2c26.25\times10^{\frac{7}{4}}=\frac{1}{{1-\frac{v^2}{c^2}}}

1v2c2=.16×1074{{1-\frac{v^2}{c^2}}}=.16\times10^{\frac{-7}{4}}

1v2c2=2.845×103{{1-\frac{v^2}{c^2}}}=2.845\times10^{-3}

v2c2=0.9971\frac{v^2}{c^2}=0.9971

vc=0.9985\frac{v}{c}=0.9985

v=0.9985cv=0.9985c


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