A Free neutron decays into a Proton, an electron and (A) \(\mathrm{v}\) (B) \(\underline{\mathrm{V}}\) (C) \(\beta\) (D) \(\alpha\)

A free neutron (n) decays into a proton (p), an electron (e⁻), and another particle which we need to identify. \(n \rightarrow p + e^- + X\) Where 'X' is the unknown particle we need to find.

A neutron decay is a common process known as beta decay (specifically, beta minus decay). In this process, a neutron changes into a proton, an electron, and an antineutrino. Let's represent the antineutrino as (\(\bar\nu_e\)). Now, let's compare this particle with the given options: (A) The first option is "\(\mathrm{v}\)" which seems to represent neutrino. (B) The second option is underlined "\(\mathrm{V}\)" which could be a different notation for a neutrino. (C) The third option is "\(\beta\)" which represents a beta particle, which is already an electron in the reaction. (D) The fourth option is "\(\alpha\)" which represents an alpha particle, which is a helium nucleus (2 protons and 2 neutrons). We are dealing with beta decay so the antineutrino is the third particle emitted during the process.

Based on our analysis, the correct particle emitted is an 'antineutrino'. The closest option to antineutrino in the list is: (B) \(\underline{\mathrm{V}}\) Thus, the answer should be option (B).