Nuclear Physics

Step 1: Concept
Nuclear reactions involve changes in the nucleus of an atom.
Step 2: Analysis
Fission specifically refers to the division of a heavy nucleus (like Uranium) into smaller nuclei with the release of energy.
Step 3: Conclusion
This process is called nuclear fission.
Final Answer: (B)

Step 1: Concept
Each -emission reduces by 2. Each -emission increases by 1.
Step 2: Analysis
Total change in .
Final atomic number .
Step 3: Conclusion
The ratio is .
Final Answer: (A)

Step 1: Concept
-decay involves the emission of an electron (or positron) from the nucleus.
Step 2: Analysis
In the given reaction, the atomic number increases by 1 ( ) while the mass number remains constant, accompanied by an electron ( ) and an antineutrino ( ).
Step 3: Conclusion
This is the characteristic equation for negative beta ( ) decay.
Final Answer: (B)

Step 1: Formula
Use the de-Broglie wavelength formula: .
Step 2: Rearrangement
.
Step 3: Substitution
.
Step 4: Calculation
kg.
Final Answer: (a)

Step 1: Nucleophilic Substitution
Heating 1,1-dichloroethane with dilute NaOH replaces both chlorine atoms with hydroxyl (-OH) groups.
Step 2: Unstable Intermediate
The resulting gem-diol (two -OH groups on the same carbon) is highly unstable.
Step 3: Dehydration
The unstable gem-diol immediately loses a water molecule to form acetaldehyde ( ).
Final Answer: (a)

Step 1: Comparison Values
The bond length of C-C in (ethane) is 1.54 Å and in (ethene) is 1.34 Å.
Step 2: Resonance Effect
In benzene, the electrons are delocalized, making all C-C bonds equivalent.
Step 3: Result
The actual carbon-carbon bond length in benzene is 1.39 Å, which lies between the single and double bond lengths.
Final Answer: (a)

Step 1: Concept
In a nuclear reaction, the sum of atomic numbers (Z) and mass numbers (A) must be conserved on both sides.
Step 2: Analysis
Atomic number: . Thus, the atomic number of X is 8.
Step 3: Conclusion
The element with atomic number 8 is Oxygen.
Final Answer: (a)

Step 1: Understand the decay process.
The decay of radioactive isotopes follows the formula: where: - is the amount of the isotope remaining at time , - is the initial amount of the isotope, - is the half-life of the isotope, and - is the time elapsed.

Step 2: Calculate the time for decay.
We are asked to find the time it takes for of the sample to decay, which means that of the sample remains. Therefore, we set: Taking the natural logarithm of both sides: Substitute :

Step 3: Conclusion.
The time for of the sample to decay is 65 h, which is option (2).

Step 1: Understand the decay process.
When Uranium-238 ( ) undergoes radioactive decay, it transforms into Protactinium-234 ( ) through a two-step process. The decay of involves the emission of an -particle, followed by the emission of a -particle.

Step 2: Explanation of emissions.
- The first step involves the emission of an -particle, which is a helium nucleus ( ), causing a decrease in the atomic number by 2 and the mass number by 4. - The second step involves the emission of a -particle, which is an electron, resulting in the conversion of a neutron into a proton.

Step 3: Conclusion.
Thus, the correct emission products in this case are an -particle and a -particle.

Step 1: Understanding the Concept:
, , and .
Step 2: Detailed Explanation:
.
Step 3: Final Answer:
Thus, .

Step 1: Understanding the Concept:
A red flower reflects red light and absorbs other colours. Green light contains no red component.
Step 2: Detailed Explanation:
Red flower appears red because it reflects red wavelength. When illuminated with green light, it absorbs green light (no red to reflect). Thus, it appears black (no light reflected).
Step 3: Final Answer:
Thus, the flower appears black.

Step 1: Understanding the Concept:
Nuclear radius follows where m, and mass .

Step 2: Detailed Explanation:
This is independent of (all nuclei have approximately the same density).

Step 3: Final Answer:
Nuclear density kg/m .

Step 1: Understanding the Concept:
For inelastic collision with hydrogen atom: neutron must supply at least excitation energy (10.2 eV). In lab frame, not all KE is available for excitation.
Step 2: Detailed Explanation:
Using conservation of momentum and energy. Masses are equal (neutron proton). Condition: . Threshold condition: . Therefore: .
Step 3: Final Answer:
Minimum kinetic energy eV.

Step 1: Understanding the Concept:
Energy produced = Power × Time. Efficiency = Output/Input.
Step 2: Detailed Explanation:
Output energy = .
Input energy = .
Energy per fission = .
Number of fissions = .
Mass of U = .
Closest is .
Step 3: Final Answer:

Step 1: For m to remain stationary relative to wedge, acceleration of wedge = acceleration of m horizontally.

Step 2: For m: , . So .

Step 3: For system: .

Step 1: Fringe width .

Step 2: If D is doubled, becomes (since original ).

Step 1: Number of atoms in 2 kg: .

Step 2: Energy = J. Power = MW.

Step 1: Understanding the Concept:
, and kWh = J.
Step 2: Detailed Explanation:
J. kWh = J. So kWh.
Step 3: Final Answer:
The energy liberated is kWh.

Step 1: Understanding the Concept:
Binding energy per nucleon is a measure of nuclear stability.
Step 2: Detailed Explanation:
The binding energy per nucleon is maximum for iron (Fe-56), which is the most stable nucleus.
Step 3: Final Answer:
The correct answer is Iron-56.

Step 1: Understanding the Concept:
Mass defect releases energy via .
Step 2: Detailed Explanation:

Energy =
This is fusion (light nuclei combining).
Step 3: Final Answer:
Fusion reaction releasing 24 MeV.

Step 1: Understanding the Concept:
Binding energy per nucleon increases to a peak then decreases.
Step 2: Detailed Explanation:
B.E./nucleon rises sharply, peaks at Fe (A=56), then slowly decreases. Curve C shows this.
Step 3: Final Answer:
Curve C is correct.

Concept:
• -particle: adds mass number 4
• Proton emission: reduces mass number by 1

Step 1: Initial mass number.


Step 2: After absorbing -particle.


Step 3: After emitting proton.