Half Life

Step 1: Understanding radioactive decay.
Radioactive decay is a process where unstable nuclei lose energy by emitting radiation. The rate of decay depends only on the number of radioactive nuclei present.

Step 2: Explanation of the reaction order.
- (1) First order reaction: Radioactive decay is a first-order reaction, where the rate of decay is directly proportional to the number of nuclei present.
- (2) Zero order reaction: Zero-order reactions are not applicable here because the rate of reaction would be independent of the concentration.
- (3) Second order reaction: Second-order reactions involve the square of the concentration, which is not the case for radioactive decay.
- (4) Third order reaction: Third-order reactions involve the cube of the concentration, which is also not applicable.

Step 3: Conclusion.
The correct answer is (1) First order reaction.

Step 1: Applying the first-order reaction formula.
For a first-order reaction, the relation between the concentration of the reactant and time is given by: where is the initial concentration, is the concentration at time , and is the rate constant.

Step 2: Substituting values.
The concentration reduces to , so: Solving for :

Step 3: Conclusion.
The time required is seconds.

Step 1: Formula / Definition}

Step 2: Calculation / Simplification}


Step 3: Final Answer

Step 1: Formula / Definition}

Step 2: Calculation / Simplification}

Let solubility :


Step 3: Final Answer

Concept: Radioactive decay with half-life: Each decay produces one -particle (He nucleus).

Step 1: Find fraction decayed in 20 days. Half-life = 10 days 2 half-lives

Step 2: Initial moles: Moles decayed:

Step 3: Moles of He formed:

Step 4: Volume at STP: Final Answer:

Concept: Probability that nucleus survives after time : After half-lives:

Step 1: After 2 half-lives


Step 2: Probability of decay
But probability of disintegration during second half-life: Conclusion:

Concept: For first order reaction: where = initial concentration, = amount reacted.

Step 1:For 90% completion:

Step 2:For 99% completion:

Step 3:Ratio: