Final answer:
Laser beam cutting provides the narrowest heat affected zone when cutting carbon steel due to its precision and minimal heat spread beyond the cut line.
Step-by-step explanation:
The cutting process that would provide the narrowest heat affected zone when cutting 12.5 mm (0.5 in) thick carbon steel is e) Laser beam cutting. Different metal cutting techniques produce varying heat affected zones (HAZ), which is the area of the base metal that is not melted but has had its microstructure and properties altered by the heat. Oxy-acetylene cutting, air-carbon arc cutting, and oxy-propane cutting employ flame or high-temperature gas streams and result in broader HAZ due to heat conduction from the cut. Plasma arc cutting reduces the HAZ compared to these methods but still generates more than desired for the narrowest HAZ. Laser cutting, on the other hand, utilizes a concentrated beam of light to achieve precision cuts with minimal kerf and HAZ, making it the most suitable among the listed options.