Atomic Structure

The decay equation for a radioactive substance is: For : For : Setting : Solving for : Thus, the correct answer is 40 s.

Step 1: The energy released during the transition is given by the Rydberg formula: Step 2: Substituting and , the energy released is: Step 3: Given that eV, we solve for : Step 4: Solving for : Thus, the correct answer is option (1), .

Step 1: Using the Rydberg Formula
For hydrogen-like species, the Rydberg formula for the wavelength of emitted photons is: where: - (Rydberg constant),
- for ,
- and are the quantum numbers of the final and initial states.
Step 2: Determining the Energy Levels
For the first transition, the given wavelength is , so: Solving for and , this corresponds to the transition from to .
For the second transition with : This corresponds to the transition from to .
Thus, the electron was initially in the state before transitioning to the ground state.
Final Answer: The principal quantum number for the excited state of is , which matches option (3).

Step 1: Use the Energy Relation for Wavelengths From energy conservation: Since energy and wavelength are related by: we get: Dividing by :
Step 2: Solve for

Energy levels for hydrogen-like atoms are given by: For Li (Z = 3), the first excited state corresponds to : Thus, the correct answer is 30.6 eV.

Step 1: Energy released per fission of Uranium is 200 MeV. Step 2: Power given as 12 MW. We convert it into joules per second: Step 3: Convert the energy released per fission into joules: Step 4: Calculate the number of fissions per second: Step 5: Total mass lost per second: Thus, the correct answer is option (4), g.