Q207 / 240 · KCET 2026 · Physics
An electron transition takes place from excited state to ground state in hydrogen atom, then
- Correct answerAIts kinetic energy increases but potential energy and total energy decrease
- BIts kinetic energy, potential energy and total energy decrease
- CKinetic energy decreases, potential energy increases but total energy remains same
- DKinetic energy and total energy decrease but potential energy increases
Solution
The total energy of an electron in the $n$-th orbit of a hydrogen atom is given by $E = -\dfrac{13.6}{n^2}$ eV.
The kinetic energy is $K = -E = \dfrac{13.6}{n^2}$ eV.
The potential energy is $U = 2E = -\dfrac{27.2}{n^2}$ eV.
When the electron transitions from an excited state to the ground state, the principal quantum number $n$ decreases.
As $n$ decreases, the value of $\dfrac{1}{n^2}$ increases. Therefore, the kinetic energy $K$ increases.
Since the total energy $E$ and potential energy $U$ are negative and their magnitudes increase, their actual values become more negative. Thus, both potential energy and total energy decrease.
Answer: Its kinetic energy increases but potential energy and total energy decrease
The kinetic energy is $K = -E = \dfrac{13.6}{n^2}$ eV.
The potential energy is $U = 2E = -\dfrac{27.2}{n^2}$ eV.
When the electron transitions from an excited state to the ground state, the principal quantum number $n$ decreases.
As $n$ decreases, the value of $\dfrac{1}{n^2}$ increases. Therefore, the kinetic energy $K$ increases.
Since the total energy $E$ and potential energy $U$ are negative and their magnitudes increase, their actual values become more negative. Thus, both potential energy and total energy decrease.
Answer: Its kinetic energy increases but potential energy and total energy decrease
Hence, the correct answer is option: 'A'.