Atom Structure Models

Step 1: Understanding the Concept:
Spectral series in hydrogen: Lyman (n=1), Balmer (n=2), Paschen (n=3), Bracket (n=4), Pfund (n=5). Transition from higher to fixed .

Step 2: Detailed Explanation:
Here, , so the series is Paschen. Transition from to gives the maximum energy and hence the shortest wavelength within the Paschen series.

Step 3: Final Answer:
The transition corresponds to the shortest wavelength of the Paschen series.

Step 1: Understanding the Concept:
Niels Bohr's model of the hydrogen atom postulates that electrons travel in discrete, quantized circular orbits. The velocity of an electron in these orbits depends on the principal quantum number ( ) and the atomic number ( ).

Step 2: Key Formula or Approach:
The theoretical derivation of the Bohr model yields the formula for the velocity ( ) of an electron in the -th orbit:

From this equation, for a specific atom where is constant, the velocity is inversely proportional to the principal quantum number :


Step 3: Detailed Explanation:
Let the speed in the first orbit ( ) be .
We want to find the speed in the third orbit, so , let's call it .
Using the inverse proportionality:


Substitute :



Step 4: Final Answer:
The speed in the 3rd orbit is .

Concept:
• Bohr radius:

Step 1: Given


Step 2: Compute
Final Conclusion:
Option (D)