Statement I: For any radioactive element the half-life is not dependent on the initial amount of the element taken

Statement II: The radioactive disintegration process is first order reaction

Statement I and statement II are correct and statement II is correct explanation of statement I

The correct answer is option 1. Statement I and statement II are correct and statement II is the correct explanation of statement I.

Statement I is correct because the half-life of a radioactive element is not dependent on the initial amount of the element taken. This is because the half-life of a radioactive element is the time it takes for half of the radioactive atoms in a sample to decay. The half-life is a characteristic of the radioactive element, and it does not depend on the amount of the element present.

Statement II is also correct because the radioactive disintegration process is a first-order reaction. This means that the rate of reaction is proportional to the concentration of the radioactive atoms. However, the half-life of a reaction is not affected by the rate of reaction. The half-life is the time it takes for half of the radioactive atoms to decay, regardless of how fast the reaction is proceeding.

Therefore, statement II is the correct explanation of statement I. The half-life of a radioactive element is not dependent on the initial amount of the element taken because the radioactive disintegration process is a first-order reaction.

Here is an example to illustrate this:

Suppose we have a sample of radioactive uranium-238 (U-238). The half-life of U-238 is 4.5 billion years. This means that if we start with a sample of 100 U-238 atoms, after 4.5 billion years, there will be 50 U-238 atoms left. After another 4.5 billion years, there will be 25 U-238 atoms left, and so on.

No matter how much U-238 we start with, the half-life will always be 4.5 billion years. This is because the half-life is a characteristic of the radioactive element, and it does not depend on the amount of the element present.