What is the speed of a proton whose kinetic energy is 5.6 keV ?
5.6 * 10^3 eV * (1.6*10^-19 Joules/ ev)
= 8.96 * 10^-16 Joules
if low compared to speed of light then
(1/2) m v^2 = (1/2)(1.67*10^-27 kg) v^2 = 8.96*10^-16
v^2 = 10.7 * 10^11 = 1.07 * 10^12
v = 1.03 * 10^6 m/s
that is far less than3*10^8 so not relativistic particularly
Well, a proton with a kinetic energy of 5.6 keV must be pretty speedy, don't you think? It's like a proton on its morning caffeine fix! But to get a better idea of its speed, we can use the equation for kinetic energy: KE = 1/2 * m * v^2.
Now, since the mass of a proton is roughly 1.67 x 10^-27 kg, we can rearrange the equation to solve for velocity. Plug in the values, do some math wizardry, and voila! You'll find that the speed of our energetic proton is about 10,719.2 km/s.
Imagine a proton zooming around at that speed! It could probably put any race car to shame. Just make sure to buckle up if you ever find yourself on the proton express!
To find the speed of a proton with a given kinetic energy, we can use the equation:
Kinetic Energy = (1/2) * mass * speed^2
First, we need to convert the kinetic energy from electronvolts (eV) to joules (J).
Given:
Kinetic energy = 5.6 keV
1 eV = 1.602 x 10^-19 J
Converting 5.6 keV to J:
1 keV = 1.602 x 10^-16 J
5.6 keV = (5.6 * 1.602) x 10^-16 J
5.6 keV = 8.99 x 10^-16 J
Now, we can use the equation to find the speed of the proton.
8.99 x 10^-16 J = (1/2) * mass * speed^2
The mass of a proton is approximately 1.67 x 10^-27 kg.
Plugging in the values:
8.99 x 10^-16 J = (1/2) * (1.67 x 10^-27 kg) * speed^2
Simplifying the equation:
17.98 x 10^-16 = (1.67 x 10^-27) * speed^2
Dividing both sides by (1.67 x 10^-27) :
17.98 x 10^-16 / (1.67 x 10^-27) = speed^2
Taking the square root:
speed = sqrt (17.98 x 10^-16 / (1.67 x 10^-27))
Calculating the result:
speed = 2.19 x 10^7 m/s
Therefore, the speed of the proton with a kinetic energy of 5.6 keV is approximately 2.19 x 10^7 m/s.
To find the speed of a proton given its kinetic energy, we can use the following equation:
KE = (1/2) * m * v^2
Where:
KE = kinetic energy of the proton
m = mass of the proton
v = speed of the proton
Since the kinetic energy is given as 5.6 keV, we need to convert it to joules. The conversion factor is 1 keV = 1.60217663 × 10^-16 J.
Therefore, the kinetic energy in joules (KE) is:
KE = 5.6 keV * (1.60217663 × 10^-16 J/1 keV) = 8.963441168 × 10^-16 J
Next, we need to determine the mass of a proton. The mass of a proton is approximately 1.67 × 10^-27 kg.
Now, we can rearrange the equation to solve for the speed (v):
v = √(2 * KE / m)
Plugging in the values we know:
v = √(2 * 8.963441168 × 10^-16 J / 1.67 × 10^-27 kg)
Simplifying this equation will give us the speed of the proton.