To determine which reaction illustrates artificial transmutation by bombardment with a neutron, let's carefully analyze each reaction provided:
1. [tex]\({}_{22}^{51} \text{Ti} \rightarrow {}_{23}^{51} \text{V} + {}_{-1}^{0} \beta\)[/tex]
This reaction describes a beta decay process, where a titanium-51 nucleus transforms into vanadium-51 by emitting a beta particle ([tex]\( \beta \)[/tex]).
2. [tex]\({}_{96}^{242} \text{Cm} \rightarrow {}_{94}^{238} \text{Pu} + {}_{2}^{4} \text{He}\)[/tex]
This reaction describes alpha decay, where a curium-242 nucleus transforms into plutonium-238 by emitting an alpha particle ([tex]\( \text{He} \)[/tex]).
3. [tex]\({}_{7}^{14} \text{N} + {}_{0}^{1} \text{n} \rightarrow {}_{6}^{14} \text{C} + {}_{1}^{1} \text{H}\)[/tex]
This reaction involves nitrogen-14 being bombarded with a neutron ([tex]\( \text{n} \)[/tex]), which results in the formation of carbon-14 and a hydrogen nucleus (a proton, [tex]\( {}_{1}^{1} \text{H} \)[/tex]). This is a clear example of artificial transmutation because it involves the bombardment of a nucleus with a neutron.
4. [tex]\({}_{96}^{242} \text{Cm} + {}_{2}^{4} \text{He} \rightarrow {}_{98}^{245} \text{Cf} + {}_{0}^{1} \text{n}\)[/tex]
This reaction describes an interaction between curium-242 and an alpha particle ([tex]\( \text{He} \)[/tex]), resulting in the formation of californium-245 and a neutron ([tex]\( \text{n} \)[/tex]). While this is a transmutation reaction, it does not specifically illustrate bombardment with a neutron.
5. [tex]\({}_{21}^{46} \text{Sc} \rightarrow {}_{21}^{46} \text{Sc} +\)[/tex] energy
This reaction describes an energy emission process without any transmutation. The scandium-46 nucleus remains the same, simply releasing energy.
Upon analyzing these reactions, the reaction that illustrates artificial transmutation by bombardment with a neutron is:
[tex]\({}_{7}^{14} \text{N} + {}_{0}^{1} \text{n} \rightarrow {}_{6}^{14} \text{C} + {}_{1}^{1} \text{H}\)[/tex]
Therefore, the correct answer is:
[tex]\[
3
\][/tex]
