By what percentage must the speed of an electron travelling at 2.968 *10⁸ m/s be increased to increase its energy by 150%? The speed of light is 2.9979 * 10⁸ m/s. A)1.4 % B)0.56 % C)0.87 % D)0.29 % E)1.0 %

Question

Quizplus · Accepted Answer

The kinetic energy of an electron is given by KE = (1/2)mv^2 where m is the mass of the electron and v is its velocity. Since the mass of an electron is constant, the only way to increase its energy by 150% is to increase its velocity.
Let the percentage increase in velocity be x. Then the new velocity of the electron is (1 + x)% of its current velocity. Therefore, the new kinetic energy of the electron is (1 + 2.5x)% of its current kinetic energy.
Since the increase in kinetic energy is 150%, we have:
(1 + 2.5x)% = 250%
Solving for x, we get x = 0.0056 or 0.56%. Therefore, the speed of the electron needs to be increased by 0.56% to increase its energy by 150%.

By What Percentage Must the Speed of an Electron Travelling