An electron is traveling at 1% the speed of light. what is its kinetic energy in joules? (Speed of light= 3x 10 to the exponent of 8 m/s)
a. 4.000 x 10-18 (exponent of -18)
b. 4.098 x 10 (exponent of -18)
c. 4.098 x 10 (exponent of 10)
d. 4.000 x 10 (exponent of 18)
To calculate the kinetic energy of an electron, we can use the equation:
Kinetic Energy = (1/2) * m * v^2
Where:
m is the mass of the electron, which is approximately 9.11 x 10^-31 kg
v is the velocity of the electron, given as 1% the speed of light, which is 0.01 * 3 x 10^8 m/s
Plugging in the values, we get:
Kinetic Energy = (1/2) * (9.11 x 10^-31) * (0.01 * 3 x 10^8)^2
Simplifying further:
Kinetic Energy = (1/2) * (9.11 x 10^-31) * (0.01)^2 * (3 x 10^8)^2
Calculating:
Kinetic Energy = (1/2) * (9.11 x 10^-31) * (0.0001) * (9 x 10^16)
Kinetic Energy = 4.09545 x 10^-46 joules
This value is closest to option a: 4.000 x 10^-18 joules.