Calculate the speed of a proton having a kinetic energy of 1.00 × 10^−19
J and a mass of 1.673 × 10^−27kg.
Answer in units of m/s
Kinetic Energy = 1/2 times m v^2
1.00 x 10^-19 = (1/2)(1.673x10^-27)v^2
solve for v^2 then take the square root to get v.
Pog PogU
To calculate the speed of a proton, you can use the formula for kinetic energy:
KE = (1/2)mv^2
where KE is the kinetic energy, m is the mass, and v is the speed.
Rearranging the equation, we get:
v = √((2KE)/m)
Given that the kinetic energy is 1.00 × 10^−19 J and the mass is 1.673 × 10^−27 kg, we can substitute these values into the equation:
v = √((2 × 1.00 × 10^−19 J) / (1.673 × 10^−27 kg))
Simplifying this calculation, we get:
v = √((2 × 1.00 × 10^−19) / (1.673 × 10^−27))
v = √(2 × 1.00 × 10^−19 / 1.673 × 10^−27)
v = √(2 × 1.00 / 1.673) × √(10^−19 / 10^−27)
v = √(1.196) × √(10^8)
v = 1.093 × 10^4 m/s
Therefore, the speed of the proton is approximately 1.093 × 10^4 m/s.
To calculate the speed of a proton, we need to use the equation for kinetic energy:
KE = 1/2 * mv^2
Where:
KE is the kinetic energy,
m is the mass, and
v is the velocity (or speed).
In this case, we are given the kinetic energy (1.00 × 10^-19 J) and the mass of the proton (1.673 × 10^-27 kg). We can rearrange the equation to solve for velocity:
v = √(2 * KE / m)
Now, substituting the given values into the equation:
v = √(2 * 1.00 × 10^-19 J / 1.673 × 10^-27 kg)
v = √(2 × 6.0 × 10^-38 m^2/s^2 / 1.673 × 10^-27 kg)
v = √(1.2 × 10^-38 m^2/s^2 / 1.673 × 10^-27 kg)
Simplifying the expression:
v = √(1.2 × 10^-38 / 1.673 × 10^-27) * (m^2/s^2 / kg)
v = √(7.18 × 10^-12) * (m^2/s^2 / kg)
v = 8.48 × 10^-6 m/s
The speed of the proton is approximately 8.48 × 10^-6 m/s.