Final answer:
The speed of a proton with a kinetic energy of 2.8 keV can be calculated by converting the energy to joules and using the relationship KE = (1/2)mv² to solve for speed.
Step-by-step explanation:
The speed of a proton which has a kinetic energy of 2.8 keV can be found using the relationship between kinetic energy (KE) and the mass (m) and speed (v) of the proton. The kinetic energy is given by the equation KE = (1/2)mv², where m is the mass of the proton (1.67 × 10⁻²⁷ kg) and v is the speed of the proton. We can rearrange this formula to solve for v: v = √(2KE/m).
First, let's convert the kinetic energy from keV to joules. 1 eV = 1.60 × 10⁻¹⁹ J, so 2.8 keV = 2.8 × 10³ eV × 1.60 × 10⁻¹⁹ J/eV = 4.48 × 10⁻¹⁶ J. Now we can plug in the values into the equation:
v = √(2 × 4.48 × 10⁻¹⁶ J / 1.67 × 10⁻²⁷ kg)
After doing the calculation, we will find the speed of the proton.