If the potential energy of an electron in the Bohr model is -U₀, then the kinetic energy and the total energy of the electron are, respectively, A) U₀ and 0.5U₀_. B) 0.5U₀ and -0.5U₀_. C) 0.5U₀ and 0.5U₀_. D) U₀ and -0.5U₀_. E) 0.5U₀ and U₀_.

Question

Quizplus · Accepted Answer

In the Bohr model, the total energy of the electron is the sum of its kinetic and potential energy. Therefore, the kinetic energy of the electron can be calculated by subtracting the potential energy from the total energy. The total energy of the electron is -U₀, as given in the problem. So, total energy = potential energy + kinetic energy => kinetic energy = total energy − potential energy = (-U₀) - (-U₀) = -U₀ + U₀ = 0 Therefore, the kinetic energy of the electron is 0. Using the formula for total energy in the Bohr model, Total energy = -hcR/n^2, where h is Planck's constant, c is the speed of light, R is the Rydberg constant, and n is the principal quantum number. From the given potential energy, we can write -hcR/n^2 = -U₀ => hcR/n^2 = U₀ Solving for n, we get n=2. Now, kinetic energy = (hcR/2n^2) − (hcR/n^2) = (hcR/4) − (hcR/2) = -0.5hcR Substituting the values of h, c, and R, we get kinetic energy = -0.5U₀_. Therefore, the kinetic energy and total energy of the electron are 0.5U₀ and -0.5U₀_., respectively, which is option B.

If the Potential Energy of an Electron in the Bohr