Statement-1:A nucleus having energy `E_(1)` decays by `beta^(-)` emission to daugther nucleus having energy `E_(2)`, but the `beta^(-)` rays are emitted with a continuous energy spectrum having end point energy `(E_(1)-E_(2))`.
Statement-2: To conserve energy and momentum in `beta`-decay, at least three particles must take part in the transformation.

Options

A. Statement-1 is correct but statement-2 is not correct
B. Statement-1 and statement-2 both are correct and statement-2 is the correct explanation of statement-1
C. Statement-1 is correct, statement is-2 is correct and statement -2 is not the correct explanation of statement-1
D. Statement-1 is incorrect, statement-2 is correct

Explanation

To solve the problem, we need to analyze both statements and determine their validity and relationship.

### Step 1: Analyze Statement 1
Statement 1 claims that a nucleus with energy \( E_1 \) decays via \( \beta^- \) emission to a daughter nucleus with energy \( E_2 \), and that the emitted \( \beta^- \) rays have a continuous energy spectrum with an endpoint energy of \( E_1 - E_2 \).

- In \( \beta^- \) decay, a neutron in the nucleus is transformed into a proton, emitting an electron (the \( \beta^- \) particle) and an antineutrino.
- The energy released in this decay is given by the difference in energy between the parent nucleus and the daughter nucleus, which is \( E_1 - E_2 \).
- The emitted electron can have a range of energies from 0 up to the maximum energy, \( E_1 - E_2 \), leading to a continuous energy spectrum.

**Conclusion for Statement 1**: True.

### Step 2: Analyze Statement 2
Statement 2 states that to conserve energy and momentum in \( \beta \) decay, at least three particles must take part in the transformation.

- In \( \beta^- \) decay, we have:
1. The daughter nucleus (which has energy \( E_2 \)),
2. The emitted electron (the \( \beta^- \) particle),
3. The antineutrino.

- The conservation of momentum requires that the momentum before the decay (which is primarily from the nucleus) equals the total momentum after the decay (which includes the momenta of the daughter nucleus, the electron, and the antineutrino).
- Similarly, energy conservation requires that the total energy before the decay equals the total energy after the decay.

**Conclusion for Statement 2**: True.

### Step 3: Determine the Relationship
Now we need to determine if Statement 2 is the correct explanation of Statement 1.

- Statement 1 describes the energy dynamics of the decay process, while Statement 2 explains the necessity of having three particles (the daughter nucleus, the emitted electron, and the antineutrino) to conserve both energy and momentum.
- Since both statements are true and Statement 2 provides a valid explanation for the phenomena described in Statement 1, we conclude that Statement 2 is indeed the correct explanation of Statement 1.

### Final Conclusion
Both statements are true, and Statement 2 is the correct explanation of Statement 1.

### Answer: Both statements are true, and Statement 2 is the correct explanation of Statement 1.

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