Atomic Models

Step 1: Understanding degeneracy.
The degeneracy of an energy level in the hydrogen atom is given by , where is the principal quantum number. For the given energy, , so the degeneracy is .

Step 2: Conclusion.
The degeneracy of the level is 9, corresponding to option (2).

Step 1: Understanding the transitions.
The wavelength of the transition is determined by the change in energy levels. For He , the wavelength of the transition from to will match the transition from to in the hydrogen spectrum.

Step 2: Conclusion.
The correct transition is from to , corresponding to option (3).

Angular momentum, mvr

Step 1: Balmer Series Formula.
The wavelength for the first emission line in the Balmer series is given by the Rydberg formula: For the first emission line, . The wave number is , and the wave number for the first emission line is .
Step 2: Conclusion.
The correct answer is (A), .

Step 1: The ionisation energy for a hydrogen-like atom is given by: For , and , so the energy is: Step 2: Converting this to joules:
Final Answer:

Using Heisenberg's uncertainty principle: The momentum , and solving for the mass gives .
Final Answer:

The energy of a photon is inversely proportional to its wavelength, given by: Since the wavelength of the second photon is twice that of the first, the energy ratio is , so the energy ratio is 4.
Final Answer:

The ratio for the electron is the highest, followed by the proton, neutron, and finally the -particle (which has a higher mass). Therefore, the increasing order is .
Final Answer: