Calculate the speed of a proton having a kinetic energy of 1.00 × 10
−19
J and a mass of
1.673 × 10
−27
kg.
Answer in units of m/s
(2*Energy/mass)^1/2=velocity
To calculate the speed of a proton, we can start by using the formula for kinetic energy:
Kinetic Energy (K) = (1/2) * mass * velocity^2
We can rearrange this equation to solve for velocity:
velocity = √(2 * kinetic energy / mass)
Now let's substitute the given values into the equation:
kinetic energy = 1.00 × 10^(-19) J
mass = 1.673 × 10^(-27) kg
Plugging these values into the equation, we get:
velocity = √(2 * 1.00 × 10^(-19) J / 1.673 × 10^(-27) kg)
Simplifying further:
velocity = √(2 * 10^(-19 - (-27)))
velocity = √(2 * 10^8)
Taking the square root:
velocity = √(2) * √(10^8)
Using a calculator or approximating, we find:
velocity ≈ 1.414 * 10^4 m/s
So, the speed of the proton is approximately 1.414 * 10^4 m/s.