An electron in a hydrogen atom undergoes a transition such that its kinetic energy increases. Let n be the principal quantum number, U be the potential energy, and E be the total energy of the electron. Which of the following is correct for this transition?

Step-by-step solution

The kinetic energy of an electron in the n^ th orbit of a hydrogen atom is given by K 1 n^2 . Since the kinetic energy increases, the principal quantum number n must decrease (the electron transitions to a lower energy level). The potential energy is U - 1 n^2 and the total energy is E - 1 n^2 . As n decreases, the magnitude 1 n^2 increases. Due to the negative sign, both U and E become more negative, which means their actual values decrease. Therefore, n decreases, U decreases, and E decreases. Answer: n decreases