Respuesta :
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
[tex]P=mv[/tex]
[tex]m =\dfrac{P}{v}[/tex]
[tex]m=\dfrac{4.350\times10^{-19}}{ 0.720\times3\times10^{8}}[/tex]
[tex]m=2.013\times10^{-27}\ Kg[/tex]
We need to calculate the rest mass of particle
Using formula of rest mass
[tex]m=\dfrac{m_{0}}{\sqrt{1-(\dfrac{v}{c})^2}}[/tex]
Where, [tex]m_{0}[/tex] = rest mass
Put the value into the formula
[tex]m_{0}=2.013\times10^{-27}\times\sqrt{1-(\dfrac{0.720 c}{c})^2}[/tex]
[tex]m_{0}=2.013\times10^{-27}\times\sqrt{1-(0.720)^2}[/tex]
[tex]m_{0}=1.4\times10^{-27}\ kg[/tex]
(b). We need to calculate the rest energy of the particle
Using formula of energy
[tex]E_{0}=m_{0}c^2[/tex]
Put the value into the formula
[tex]E_{0}=1.4\times10^{-27}\times(3\times10^{8})^2[/tex]
[tex]E_{0}=1.26\times10^{-10}\ J[/tex]
(c). We need to calculate the kinetic energy of the particle
Using formula of kinetic energy
[tex]K.E=mc^2-m_{0}c^2[/tex]
[tex]K.E=(m-m_{0})\timesc^2[/tex]
[tex]K.E=(2.013\times10^{-27}-1.4\times10^{-27})\times3\times10^{8}[/tex]
[tex]K.E=1.84\times10^{-19}\ J[/tex]
(d). We need to calculate the total energy of the particle
Using formula of energy
[tex]E=mc^2[/tex]
Put the value into the formula
[tex]E=2.013\times10^{-27}\times(3\times10^{8})^2[/tex]
[tex]E=1.812\times10^{-10}\ J[/tex]
Hence, This is the required solution.
