Atomic Spectra

For minimum wavelength,

As we know that time period of revolution of an electron is
,
And and
and for -atom

Step 1: Understanding the Question:
The goal is to determine how the kinetic, potential, and total energy of an electron change when it moves from a higher energy level (excited state) to a lower energy level (ground state).
Step 2: Key Formula or Approach:
For an electron in the -th orbit of a hydrogen atom:
- Total Energy:
- Kinetic Energy:
- Potential Energy:
Step 3: Detailed Explanation:
Transition is from an excited state (higher ) to the ground state ( ).
1. Total Energy ( ): As decreases, increases. Since is negative, a larger numerical value means a decrease (it becomes more negative).
2. Kinetic Energy ( ): is positive and proportional to . As decreases, increases.
3. Potential Energy ( ): Since is negative and proportional to , as decreases, decreases (it becomes more negative).
Comparing with options, statement (1) is correct.
Step 4: Final Answer:
Upon transition to a lower state, kinetic energy increases while potential and total energy decrease. This is option (1).