Which of the following assertions are correct?
(i) A neutron can decay to a proton only inside a nucleus
(ii) A proton can change to a neutron only inside a nucleus
(iii) An isolated neutron can change into a proton
(iv) An isolated proton can change into a neutron

Answer

To determine which assertions are correct, we will analyze each statement one by one based on our understanding of nuclear physics, particularly beta decay processes.

### Step-by-Step Solution:

1. **Assertion (i): A neutron can decay to a proton only inside a nucleus.**
- This assertion is **incorrect**. A neutron can decay into a proton through beta decay, which occurs outside of a nucleus as well. An isolated neutron is unstable and will decay into a proton, an electron, and an antineutrino.

2. **Assertion (ii): A proton can change to a neutron only inside a nucleus.**
- This assertion is **correct**. A proton can change into a neutron through a process called beta plus decay (β+ decay), which requires the presence of other nucleons (neutrons) and cannot occur in isolation due to energy constraints. This process typically occurs in a nucleus where the binding energy allows such transformations.

3. **Assertion (iii): An isolated neutron can change into a proton.**
- This assertion is **correct**. An isolated neutron is unstable and will eventually decay into a proton, an electron, and an antineutrino. This decay occurs spontaneously and does not require a nucleus.

4. **Assertion (iv): An isolated proton can change into a neutron.**
- This assertion is **incorrect**. An isolated proton cannot change into a neutron without the involvement of a nucleus. The transformation from a proton to a neutron (β+ decay) requires conditions that are only found within a nucleus, as it involves the conversion of a proton into a neutron and the emission of a positron and a neutrino.

### Summary of Correct Assertions:
- Correct Assertions: (ii) and (iii)
- Incorrect Assertions: (i) and (iv)