KCET · Physics · Atomic Physics
An electron transition takes place from excited state to ground state in hydrogen atom, then
- A Its kinetic energy increases but potential energy and total energy decrease
- B Its kinetic energy, potential energy and total energy decrease
- C Kinetic energy decreases, potential energy increases but total energy remains same
- D Kinetic energy and total energy decrease but potential energy increases
Answer & Solution
Correct Answer
(A) Its kinetic energy increases but potential energy and total energy decrease
Step-by-step Solution
Detailed explanation
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
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