A certain moving electron has a kinetic energy
of 0.991 × 10−19 J.
Calculate the speed necessary for the electron to have this energy. The mass of an
electron is 9.109 × 10−31 kg.
Answer in units of m/s.
answer is ?
K.E. = 1/2 m v^2 ... v = √(2 K.E. / m)
To find the speed necessary for the electron to have a kinetic energy of 0.991 × 10^-19 J, you can use the equation:
Kinetic Energy = (1/2) * mass * speed^2
Rearranging the equation, we get:
speed = sqrt((2 * Kinetic Energy) / mass)
Now, let's substitute the given values:
mass of electron (m) = 9.109 × 10^-31 kg
Kinetic Energy = 0.991 × 10^-19 J
Plugging these values into the equation, we have:
speed = sqrt((2 * 0.991 × 10^-19 J) / (9.109 × 10^-31 kg))
Calculating the expression inside the square root:
speed = sqrt(2.1789 * 10^12 m^2/s^2 / 9.109 × 10^-31 kg)
Dividing the numerator by the denominator:
speed = sqrt(2.392 * 10^42 m^2/s^2)
Taking the square root:
speed ≈ 4.891 × 10^21 m/s
Therefore, the speed necessary for the electron to have a kinetic energy of 0.991 × 10^-19 J is approximately 4.891 × 10^21 m/s.