Nuclear Physics

We know that the neutrino is the particle which has almost zero mass and exactly zero charge. Positron has the charge and mass [equal to electron mass].
Electron is a particle which has - charge and mass.
Neutron is a particle which has zero charge and mass.
So, the required answer is neutrino.

Step 1: Formula for radioactive decay.
The number of nuclei decayed over time can be calculated using the formula for half-life decay: where is the initial number of nuclei, is the time elapsed, and is the half-life of the element. The number of nuclei decayed is given by: Step 2: Applying the given values.
Given that , days, and days, we first find the number of remaining nuclei after 60 days: Thus, the number of nuclei decayed is: Step 3: Conclusion.
Thus, the number of nuclei decayed after 60 days is , corresponding to option (C).

Step 1: Relation between decay constant and half-life.


Step 2: Expression for activity.
Activity is given by:


Step 3: Instantaneous rate of change of activity.


Step 4: Substitute relation with half-life.


Step 5: Conclusion.
The instantaneous rate of change of activity is proportional to .

Step 1: Understanding the decay process.
In radioactive decay, the decay rate is proportional to the number of active nuclei . This means the more the active nuclei, the higher the decay rate.
Step 2: Analyzing the graphs.
- In Graph A, the decay rate increases with the number of active nuclei and then decreases, which is characteristic of the exponential decay process where the decay rate initially increases and then decreases as the number of nuclei reduces. - Graph B shows a linear relationship, which is not characteristic of the decay process. - Graph C shows a rapid increase followed by a sharp decrease, which is not correct for radioactive decay. - Graph D shows a constant decay rate, which is also not accurate.
Step 3: Conclusion.
Graph A correctly represents the variation of decay rate with the number of active nuclei. This corresponds to option (C).

The formula for half-life decay is: where:
- is the remaining quantity after time ,
- is the initial quantity,
- is the half-life of the substance. Given that years and the initial weight is 64 gm, after 15 years: Thus, the remaining weight after 15 years is 8 gm.

The nuclear density ( ) remains approximately constant across all nuclei, regardless of atomic number or mass number. This invariance arises from the proportional relationship between the nuclear mass and volume with the mass number ( ). 1. Nuclear Density for : For , the mass number . The nuclear density is: 2. Nuclear Density for : For , the mass number . The nuclear density remains the same as that of : 3. Ratio of Densities: As the nuclear density is constant for all nuclei: Final Answer: