Respuesta :
Answer:
The non-relativistic kinetic energy of a proton is [tex]6.76\times10^{-12}\ J[/tex]
The relativistic kinetic energy of a proton is [tex]7.25\times10^{-12}\ m/s[/tex]
Explanation:
Given that,
Mass of proton [tex]m=1.67\times10^{-27}\ kg[/tex]
Speed [tex]v= 9.00\times10^{7}\ m/s[/tex]
We need to calculate the kinetic energy for non relativistic
Using formula of kinetic energy
[tex]K.E=\dfrac{1}{2}mv^2[/tex]
Put the value into the formula
[tex]K.E=\dfrac{1}{2}\times1.67\times10^{-27}\times(9.00\times10^{7})^2[/tex]
[tex]K.E=6.76\times10^{-12}\ J[/tex]
We need to calculate the kinetic energy for relativistic
Using formula of kinetic energy
[tex]K.E=mc^2(\sqrt{(\dfrac{1}{1-\dfrac{v^2}{c^2}})}-1)[/tex]
[tex]K.E=1.67\times10^{-27}\times(3\times10^{8})^{2}\cdot\left(\sqrt{\frac{1}{1-\frac{\left(9.00\times10^{7}\right)^{2}}{(3\times10^{8})^{2}}}}-1\right)[/tex]
[tex]K.E=7.25\times10^{-12}\ m/s[/tex]
Hence, The non-relativistic kinetic energy of a proton is [tex]6.76\times10^{-12}\ J[/tex]
The relativistic kinetic energy of a proton is [tex]7.25\times10^{-12}\ m/s[/tex]
