An electron in a hydrogen atom makes a transition to a higher energy level. Let be the de Broglie wavelength of the electron, T be its time period of revolution, and be its angular velocity in the orbit. Which of the following correctly describes the changes in these quantities?

Step-by-step solution

For an electron in the n^ th orbit of a hydrogen atom, the orbital radius is r n^2 and the orbital speed is v 1 n . When the electron transitions to a higher energy level, the principal quantum number n increases. 1. The de Broglie wavelength is = h mv 1 v n . As n increases, increases. 2. The time period of revolution is T = 2 r v n^2 1/n = n^3 . As n increases, T increases. 3. The angular velocity is = v r 1/n n^2 = 1 n^3 . As n increases, decreases. Thus, increases, T increases, and decreases. Answer: increases,