What is the speed of a proton whose kinetic energy is 12.9 keV?

Well, I'm not sure if protons go to the gym, but let's calculate their speed anyway! So, to find the speed of a proton given its kinetic energy, we can use the formula 1/2mv^2 = KE, where m is the mass of the proton and v is its velocity. Since we're given the kinetic energy as 12.9 keV, we just need to find the mass of a proton (which is approximately 1.67 x 10^-27 kg) and rearrange the formula to solve for v. But before I continue, I must admit, I'm more of a circus clown than a physics whiz. Go ahead, ask me another question!

To find the speed of a proton with a given kinetic energy, you can use the following steps:

Step 1: Convert the kinetic energy from electron volts (eV) to joules (J).

1 eV = 1.602 × 10^-19 J

Given kinetic energy: 12.9 keV

Converting to joules:
12.9 keV × 1.602 × 10^-19 J/eV = 2.07 × 10^-18 J

Step 2: Use the kinetic energy formula to find the speed (v) of the proton.

The kinetic energy (K) of an object is given by the formula:

K = (1/2)mv^2

Where:
K = kinetic energy
m = mass of the object
v = velocity (speed) of the object

Since the mass of a proton is approximately 1.67 × 10^-27 kg, we can rearrange the formula to solve for v:

v = √((2K) / m)

Using the given kinetic energy (K = 2.07 × 10^-18 J) and the proton mass (m = 1.67 × 10^-27 kg), we can now calculate the speed (v).

v = √((2 × 2.07 × 10^-18 J) / (1.67 × 10^-27 kg))

Calculating this expression gives us:

v ≈ 2.75 × 10^7 m/s

Therefore, the speed of a proton with a kinetic energy of 12.9 keV is approximately 2.75 × 10^7 m/s.

To determine the speed of a proton with a given kinetic energy, we can use the formula for kinetic energy:

KE = (1/2)mv^2

where KE is the kinetic energy, m is the mass of the proton, and v is the speed of the proton.

In this case, we are given that the kinetic energy is 12.9 keV. However, we need to convert this value to joules since the SI unit of energy is the joule.

To convert keV to joules, we know that 1 keV is equal to 1.6 x 10^-16 joules.

So, the kinetic energy in joules is calculated as follows:

KE_joules = 12.9 keV * (1.6 x 10^-16 J/1 keV) = 2.064 x 10^-15 J

Next, we need to determine the mass of a proton. The mass of a proton is approximately 1.67 x 10^-27 kg.

Now, we can rearrange the kinetic energy formula to solve for velocity (v):

v = sqrt((2 * KE) / m)

Substituting the values, we have:

v = sqrt((2 * 2.064 x 10^-15 J) / 1.67 x 10^-27 kg)

v = sqrt(2.478 x 10^12 m^2/s^2) = 1.58 x 10^6 m/s

Therefore, the speed of the proton with a kinetic energy of 12.9 keV is approximately 1.58 x 10^6 m/s.

Kinetic energy is 1/2 m v^2

1 eV = 1.6 * 10^-19 Joule so
12.9 keV = 2.0668 * 10^-15 Joule
mass of proton = 1.67 * 10^-27 kg
substituting

v^2 = 2 * 2.0668 * 10^-15/(1.67 * 10^-27)
v^2 = 2.475 * 10^12
v = sqrt(2.475 * 10^12)
v = 1.57 * 10^6 m/sec