Understand what a $\beta$-particle is

In nuclear radioactivity, a $\beta$-particle usually means a $\beta^-$ particle, which is an electron emitted from the nucleus.

Process responsible for $\beta^-$ emission

In $\beta^-$ decay, a neutron converts into a proton inside the nucleus:

$n \rightarrow p + e^- + \bar{\nu}$

Here:

• $n$ = neutron
• $p$ = proton
• $e^-$ = $\beta$-particle
• $\bar{\nu}$ = antineutrino

Check each option

• A: conversion of proton to neutron
  This corresponds to $\beta^+$ decay / positron-related process, not ordinary $\beta^-$ emission. So this is incorrect.

• B: from outermost orbit
  A $\beta$-particle is not emitted from electronic orbit, but from the nucleus. So this is incorrect.

• C: conversion of neutron to proton
  This is exactly the process of $\beta^-$ decay. So this is correct.

• D: $\beta$-particle is not emitted
  This is clearly incorrect.

Final answer

The correct option is:

$\boxed{\text{C}}$

Comparison with stored correct answer

Stored correct answer = C
Derived answer = C
Hence, they agree.