Bohr Model Of The Hydrogen Atom

Concept: In the Bohr model of hydrogen atom:

Energy of nth orbit:
Angular momentum:

Step 1: Identify orbit number. Given energy: Using:
Step 2: Angular momentum. Using Bohr quantization:
Step 3: Match with options. From given choices, corresponds to option (C). But angular momentum is often written as multiples of : Closest listed Bohr-multiple form is: Final Answer:

Concept: The radius of a nucleus is given by the empirical formula: Where:


= mass number

Step 1: Substitute the given mass number.
Step 2: Evaluate cube root.
Step 3: Calculate radius. Using the commonly accepted approximation :
Step 4: Choose the closest option. The nearest value is .

Concept: The binding energy per nucleon curve explains nuclear stability:

Peaks around iron ( )
Light nuclei gain stability by fusion
Heavy nuclei gain stability by fission

Step 1: Analyze Assertion (A).

Heavy nuclei (like uranium) split → higher binding energy per nucleon → energy released (fission)
Light nuclei (like hydrogen isotopes) combine → higher binding energy per nucleon → energy released (fusion)
Thus, Assertion is true.
Step 2: Analyze Reason (R). The reason claims:

Binding energy per nucleon increases with increasing for heavy nuclei
Decreases with increasing for light nuclei
This is incorrect. Actual trend:

Binding energy per nucleon increases with mass number up to iron
Then decreases for heavier nuclei
So the given reasoning is false.
Step 3: Conclusion.

Assertion → True
Reason → False
Hence, option (C).