How do you show that the kinetic energy is equal to the atoms rest energy when its velocity equals .886 times the speed of light?
Thanks in advanced!
To show that the kinetic energy of an atom is equal to its rest energy when its velocity is 0.886 times the speed of light, we can use Einstein's theory of relativity.
Let's start by defining the kinetic energy (KE) and rest energy (E) of an atom. The kinetic energy of an object is given by the equation:
KE = (1/2) * m * v^2
where m is the mass of the object and v is its velocity. The rest energy of an object is given by Einstein's famous equation:
E = m * c^2
where m is the mass of the object and c is the speed of light.
Now, let's substitute the given value of velocity, which is 0.886 times the speed of light, into the equation for kinetic energy:
KE = (1/2) * m * (0.886c)^2
Simplifying this equation, we have:
KE = (1/2) * m * (0.886^2) * c^2
Next, let's substitute the equation for rest energy into the expression for kinetic energy:
KE = (1/2) * (E / c^2) * (0.886^2) * c^2
KE = (1/2) * E * (0.886^2)
Finally, let's check if the kinetic energy is equal to the rest energy:
If KE = E, then:
(1/2) * E * (0.886^2) = E
(1/2) * (0.886^2) = 1
0.781156 = 1
Since 0.781156 is not equal to 1, it means that the kinetic energy of an atom is not equal to its rest energy when its velocity is 0.886 times the speed of light.
So, in this case, the kinetic energy is not equal to the rest energy of the atom.