Describe how you might use radioactive materials to find a leak in the \(\mathrm{H}_{2}(\mathrm{g})\) supply line in an ammonia synthesis plant.

In the industrial sphere, radioisotopes offer remarkable benefits due to their unique properties. One of the most practical applications is in the detection and analysis of hidden problems within systems, such as leaks in pipes.

These isotopes, when introduced into a system, emit radiation that can be traced using specialized detectors. Their journey through pipes or enclosed systems can be monitored, and any unusual dispersal of radiation can point to issues like cracks or leaks. It's a non-invasive and highly efficient method, as the isotopes can travel through areas that are typically tough to inspect manually or visually.

This use of radioisotopes is prevalent in various industries, including oil and gas, chemical manufacturing, and power generation. It provides a safer, quicker, and often more cost-effective solution compared to traditional methods.

Tritium, or hydrogen-3, is a unique isotope of hydrogen consisting of one proton and two neutrons, which makes it radioactive. As a beta emitter, its radiation can be easily detected, but it doesn't penetrate materials deeply, making it relatively safe to use under controlled conditions.

Its properties make it ideal for applications like leak detection in pipelines. When mixed with hydrogen gas—as it is an isotope of hydrogen—it becomes a part of the gas flow, allowing it to indicate the presence and location of leaks. Tritium's half-life of about 12.3 years ensures that it remains active long enough to be useful in such applications, but not so long that it poses extended risks.

Radiation detection is a critical component when using radioisotopes for industrial applications. Specialized equipment is used to detect and measure radiation levels, with different detectors designed to identify various types of radiation.

For beta emissions, like those from tritium, instruments like Geiger-Müller counters or scintillation detectors are commonly used. The readings from these detectors can help technicians identify discrepancies that suggest the presence of leaks. It's important that these detectors are sensitive and accurate, to ensure safety and reliability in detecting even small traces of radiation that may indicate a problem within the system.

The role of radioactivity in industrial applications extends far beyond leak detection. Other uses include material thickness measurement, where radioisotopes help ensure quality control in the production of materials like paper, plastic, and metal. Radioactive sources are also used in radiography to inspect welds and internal components for defects.

Moreover, radioactivity is utilized in the sterilization of medical equipment and food preservation, showcasing its versatility. In all these applications, the benefits hinge on the ability of radioactive materials to penetrate different substances, providing an internal view or altering material properties without direct contact or the need for disruptive processes.