Respuesta :
Answer:
The fraction of its energy that it radiates every second is [tex]3.02\times10^{-11}[/tex].
Explanation:
Suppose Electromagnetic radiation is emitted by accelerating charges. The rate at which energy is emitted from an accelerating charge that has charge q and acceleration a is given by
[tex]\dfrac{dE}{dt}=\dfrac{q^2a^2}{6\pi\epsilon_{0}c^3}[/tex]
Given that,
Kinetic energy = 6.2 MeV
Radius = 0.500 m
We need to calculate the acceleration
Using formula of acceleration
[tex]a=\dfrac{v^2}{r}[/tex]
Put the value into the formula
[tex]a=\dfrac{\dfrac{1}{2}mv^2}{\dfrac{1}{2}mr}[/tex]
Put the value into the formula
[tex]a=\dfrac{6.2\times10^{6}\times1.6\times10^{-19}}{\dfrac{1}{2}\times1.67\times10^{-27}\times0.51}[/tex]
[tex]a=2.32\times10^{15}\ m/s^2[/tex]
We need to calculate the rate at which it emits energy because of its acceleration is
[tex]\dfrac{dE}{dt}=\dfrac{q^2a^2}{6\pi\epsilon_{0}c^3}[/tex]
Put the value into the formula
[tex]\dfrac{dE}{dt}=\dfrac{(1.6\times10^{-19})^2\times(2.3\times10^{15})^2}{6\pi\times8.85\times10^{-12}\times(3\times10^{8})^3}[/tex]
[tex]\dfrac{dE}{dt}=3.00\times10^{-23}\ J/s[/tex]
The energy in ev/s
[tex]\dfrac{dE}{dt}=\dfrac{3.00\times10^{-23}}{1.6\times10^{-19}}\ J/s[/tex]
[tex]\dfrac{dE}{dt}=1.875\times10^{-4}\ ev/s[/tex]
We need to calculate the fraction of its energy that it radiates every second
[tex]\dfrac{\dfrac{dE}{dt}}{E}=\dfrac{1.875\times10^{-4}}{6.2\times10^{6}}[/tex]
[tex]\dfrac{\dfrac{dE}{dt}}{E}=3.02\times10^{-11}[/tex]
Hence, The fraction of its energy that it radiates every second is [tex]3.02\times10^{-11}[/tex].
