A: A radioactive substance has half life of 4 hour. Therefore, if two nuclei of the substance are present initially , after 1 hour only one will remain undissociated.
R: When a nucleus makes a transition from excited state to ground state, it emits a `beta`-particle.

Options

A. if both assertion & reason are true and the reason is correct explanation of the assertion then mark (1)
B. if both assertion & reason are true and the reason is not correct explanation of the assertion then mark (2)
C. if assertion is true statement but reason is false then mark (3)
D. if both assertion & reason are false then mark (4)

Answer

To solve the problem, we need to analyze both the assertion and the reason provided.

### Step 1: Analyze the Assertion
The assertion states that a radioactive substance has a half-life of 4 hours. If there are initially 2 nuclei, then after 1 hour, only one will remain undissociated.

- **Understanding Half-Life**: The half-life of a radioactive substance is the time required for half of the radioactive nuclei in a sample to decay. In this case, the half-life is 4 hours.
- **Initial Nuclei**: We start with 2 nuclei.
- **After 1 hour**: Since 1 hour is not equal to the half-life (4 hours), we cannot determine the number of nuclei remaining after just 1 hour using the half-life concept. The decay process is probabilistic, and we cannot conclude that one nucleus will remain undissociated after just 1 hour.

### Conclusion for Assertion
After 1 hour, we cannot say that only one nucleus will remain undissociated. Therefore, the assertion is **false**.

### Step 2: Analyze the Reason
The reason states that when a nucleus makes a transition from an excited state to the ground state, it emits a beta particle.

- **Understanding Transitions**: When a nucleus transitions from an excited state to a ground state, it typically emits energy in the form of gamma rays, not beta particles. Beta decay involves the transformation of a neutron into a proton (or vice versa) and the emission of a beta particle (an electron or positron), which is a different process.

### Conclusion for Reason
The reason provided is also **false** because the emission of beta particles is not associated with the transition from an excited state to the ground state.

### Final Conclusion
Both the assertion and the reason are false. Therefore, the correct answer is that both statements are incorrect.

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