X-rays form ionizing radiation that is dangerous to living tissue and undetectable to the human eye. Suppose that a student researcher working in an X-ray diffraction laboratory is accidentally exposed to a fatal dose of radiation. Calculate the temperature increase of the researcher under the following conditions: the energy of X-ray photons is \(200 \mathrm{keV}\) and the researcher absorbs \(4 \times 10^{13}\) photons per each kilogram of body weight during the exposure. Assume that the specific heat of the student's body is \(0.83 \mathrm{kcal} / \mathrm{kg} \cdot \mathrm{K}\).

Ionizing radiation refers to the type of radiation that has enough energy to remove tightly bound electrons from their atoms, creating ions. Sources of ionizing radiation include radioactive materials, cosmic rays, and X-ray machines, such as those found in X-ray diffraction laboratories. When living tissues are exposed to ionizing radiation, it can lead to cellular damage, cancer, and even death, which is why it is considered dangerous. Safety protocols in laboratories, such as time, distance, and shielding, are critical in reducing the exposure and protecting researchers from its harmful effects.

Unlike light or heat, ionizing radiation is not detectable by human senses. Therefore, labs must equip themselves with radiation detection instruments to monitor exposure levels. Appropriate personal protective equipment (PPE) and rigorous safety training are vital for anyone working around ionizing radiation to avoid accidents like the one described in the exercise.

Energy possessed by a photon is directly proportional to its electromagnetic wave frequency and inversely proportional to wavelength. The energy of a photon can be calculated using the formula:
\[ E = hf \]
where \( E \) is the energy, \( h \) is Planck's constant, and \( f \) is the frequency. Calculating photon energy is essential in understanding the amount of energy that each X-ray photon has, which is significant when assessing exposure levels and potential biological effects. In our case, X-ray photons are given a specific energy of 200 keV (kilo-electron volts), which must be converted into joules (J), the standard scientific unit for energy, to calculate the absorbed dose by the researcher. The conversion factor (\(1.6\times10^{-13}\) J/keV) bridges these units to ensure that the energy absorbed calculations are accurate.

Specific heat capacity is the amount of heat needed to raise the temperature of a unit of mass by one degree Celsius (or one Kelvin). Different substances have various specific heats, indicating their ability to absorb heat. Water, for example, has a high specific heat and can absorb a lot of heat before its temperature increases significantly. In the context of our exercise, we assess the impact of absorbed radiation by the researcher's body through a temperature change. To calculate the temperature change (\( \Delta T \)) we use the equation:
\[ \Delta T = \frac{E_{absorbed}}{specific \, heat}\]
This equation helps us understand that the energy deposited by the X-ray photons in the researcher's body causes a temperature rise, denoted here as 0.368 K. The mass of the researcher cancels out, assuming the specific heat capacity is uniform throughout the body. Hence, this illustrative temperature change serves as an abstract means to grasp the concept of heat absorption due to radiation exposure.