Question

Particle-X has a speed of 0.720 c and a momentum of 4.350x1019 kgm/s. What is the mass of the particle? 2.0206 10-27 kg Hints: The classical momentum of an object is the product of its mass and its velocity. How does the relativistic momentum look like comp classical momentum? Submit Answer Incorrect. Tries 2/12 PreviouS Tries What is the rest energy of the particle? Submit Answer Tries 0/12 What is the kinetic energy of the particle? Submit Answer Tries 0/12 What is the total energy of the particle?

Answer 1

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

$P=mv$

$m =\dfrac{P}{v}$

$m=\dfrac{4.350\times10^{-19}}{ 0.720\times3\times10^{8}}$

$m=2.013\times10^{-27}\ Kg$

We need to calculate the rest mass of particle

Using formula of rest mass

$m=\dfrac{m_{0}}{\sqrt{1-(\dfrac{v}{c})^2}}$

Where, $m_{0}$ = rest mass

Put the value into the formula

$m_{0}=2.013\times10^{-27}\times\sqrt{1-(\dfrac{0.720 c}{c})^2}$

$m_{0}=2.013\times10^{-27}\times\sqrt{1-(0.720)^2}$

$m_{0}=1.4\times10^{-27}\ kg$

(b). We need to calculate the rest energy of the particle

Using formula of energy

$E_{0}=m_{0}c^2$

Put the value into the formula

$E_{0}=1.4\times10^{-27}\times(3\times10^{8})^2$

$E_{0}=1.26\times10^{-10}\ J$

(c).  We need to calculate the kinetic energy of the particle

Using formula of kinetic energy

$K.E=mc^2-m_{0}c^2$

$K.E=(m-m_{0})\timesc^2$

$K.E=(2.013\times10^{-27}-1.4\times10^{-27})\times3\times10^{8}$

$K.E=1.84\times10^{-19}\ J$

(d). We need to calculate the total energy of the particle

Using formula of energy

$E=mc^2$

Put the value into the formula

$E=2.013\times10^{-27}\times(3\times10^{8})^2$

$E=1.812\times10^{-10}\ J$

Hence, This is the required solution.