Explanation:
Given that,
Speed of particle = 0.720 c
Momentum = 4.350\times10^{-19}\ kgm/s[/tex]
(I). We need to calculate the mass of the particle
Using formula of momentum
![P=mv](https://tex.z-dn.net/?f=P%3Dmv)
![m =\dfrac{P}{v}](https://tex.z-dn.net/?f=m%20%3D%5Cdfrac%7BP%7D%7Bv%7D)
![m=\dfrac{4.350\times10^{-19}}{ 0.720\times3\times10^{8}}](https://tex.z-dn.net/?f=m%3D%5Cdfrac%7B4.350%5Ctimes10%5E%7B-19%7D%7D%7B%200.720%5Ctimes3%5Ctimes10%5E%7B8%7D%7D)
![m=2.013\times10^{-27}\ Kg](https://tex.z-dn.net/?f=m%3D2.013%5Ctimes10%5E%7B-27%7D%5C%20Kg)
We need to calculate the rest mass of particle
Using formula of rest mass
![m=\dfrac{m_{0}}{\sqrt{1-(\dfrac{v}{c})^2}}](https://tex.z-dn.net/?f=m%3D%5Cdfrac%7Bm_%7B0%7D%7D%7B%5Csqrt%7B1-%28%5Cdfrac%7Bv%7D%7Bc%7D%29%5E2%7D%7D)
Where,
= rest mass
Put the value into the formula
![m_{0}=2.013\times10^{-27}\times\sqrt{1-(\dfrac{0.720 c}{c})^2}](https://tex.z-dn.net/?f=m_%7B0%7D%3D2.013%5Ctimes10%5E%7B-27%7D%5Ctimes%5Csqrt%7B1-%28%5Cdfrac%7B0.720%20c%7D%7Bc%7D%29%5E2%7D)
![m_{0}=2.013\times10^{-27}\times\sqrt{1-(0.720)^2}](https://tex.z-dn.net/?f=m_%7B0%7D%3D2.013%5Ctimes10%5E%7B-27%7D%5Ctimes%5Csqrt%7B1-%280.720%29%5E2%7D)
![m_{0}=1.4\times10^{-27}\ kg](https://tex.z-dn.net/?f=m_%7B0%7D%3D1.4%5Ctimes10%5E%7B-27%7D%5C%20kg)
(b). We need to calculate the rest energy of the particle
Using formula of energy
![E_{0}=m_{0}c^2](https://tex.z-dn.net/?f=E_%7B0%7D%3Dm_%7B0%7Dc%5E2)
Put the value into the formula
![E_{0}=1.4\times10^{-27}\times(3\times10^{8})^2](https://tex.z-dn.net/?f=E_%7B0%7D%3D1.4%5Ctimes10%5E%7B-27%7D%5Ctimes%283%5Ctimes10%5E%7B8%7D%29%5E2)
![E_{0}=1.26\times10^{-10}\ J](https://tex.z-dn.net/?f=E_%7B0%7D%3D1.26%5Ctimes10%5E%7B-10%7D%5C%20J)
(c). We need to calculate the kinetic energy of the particle
Using formula of kinetic energy
![K.E=mc^2-m_{0}c^2](https://tex.z-dn.net/?f=K.E%3Dmc%5E2-m_%7B0%7Dc%5E2)
![K.E=(m-m_{0})\timesc^2](https://tex.z-dn.net/?f=K.E%3D%28m-m_%7B0%7D%29%5Ctimesc%5E2)
![K.E=(2.013\times10^{-27}-1.4\times10^{-27})\times3\times10^{8}](https://tex.z-dn.net/?f=K.E%3D%282.013%5Ctimes10%5E%7B-27%7D-1.4%5Ctimes10%5E%7B-27%7D%29%5Ctimes3%5Ctimes10%5E%7B8%7D)
![K.E=1.84\times10^{-19}\ J](https://tex.z-dn.net/?f=K.E%3D1.84%5Ctimes10%5E%7B-19%7D%5C%20J)
(d). We need to calculate the total energy of the particle
Using formula of energy
![E=mc^2](https://tex.z-dn.net/?f=E%3Dmc%5E2)
Put the value into the formula
![E=2.013\times10^{-27}\times(3\times10^{8})^2](https://tex.z-dn.net/?f=E%3D2.013%5Ctimes10%5E%7B-27%7D%5Ctimes%283%5Ctimes10%5E%7B8%7D%29%5E2)
![E=1.812\times10^{-10}\ J](https://tex.z-dn.net/?f=E%3D1.812%5Ctimes10%5E%7B-10%7D%5C%20J)
Hence, This is the required solution.