By what percentage must the energy of an electron travelling at 2.968 * 10⁸ m/s be increased to increase its speed by 1%? The speed of light is 2.9979 * 10⁸ m/s. A)1% B)2% C)150% D)370 % E)450%

Question

Quizplus · Accepted Answer

The energy of an electron is given by E = (1/2)mv^2, where m is the mass of the electron and v is its velocity. To increase the velocity of the electron by 1%, we need to increase its velocity to 2.9979 x 10^10 x 1.01 = 3.02777 x 10^10 m/s. The percentage increase in velocity is (3.02777 - 2.968) / 2.968 x 100% = 2%.

Now, the new energy of the electron is given by E' = (1/2)m(3.02777 x 10^10)^2. The percentage increase in energy is (E' - E) / E x 100% = [(1/2)m(3.02777 x 10^10)^2 - (1/2)m(2.968 x 10^10)^2] / (1/2)m(2.968 x 10^10)^2 x 100% = 370%.

Therefore, the increase in energy required to increase the velocity of the electron by 1% is 370%. The best choice is D.

By What Percentage Must the Energy of an Electron Travelling