Roentgen Conversion to SI Units Explained

The question asks for the value of one roentgen (R) expressed in the International System of Units (SI). The roentgen is a historical unit used to measure the exposure dose of X-rays and gamma rays.

Understanding Radiation Units

It's important to know the different units used in radiation measurement:

• Roentgen (R): Measures the exposure dose of X-rays or gamma rays in air. It quantifies the ionization produced in air by the radiation.
• Gray (Gy): The SI unit for absorbed dose. It measures the amount of radiation energy deposited in a material (like tissue). 1 Gy = 1 Joule/kilogram.
• Coulomb per kilogram (C/kg): The SI unit for exposure*. It measures the total charge of ions of one sign produced in air by photons per unit mass of air.
• Becquerel (Bq): The SI unit for radioactivity (activity). It measures the rate of radioactive decay. 1 Bq = 1 disintegration per second.

Roentgen to SI Unit Conversion

The roentgen (R) is not an SI unit. The SI unit that measures the same physical quantity (exposure) is the Coulomb per kilogram (C/kg).

The conversion factor is defined as:

$1 R = 2.58 × 10^-4 C/kg$

This value represents the amount of X-ray or gamma radiation that produces an electrical charge of 2.58 × 10^-4 coulombs in 1 kilogram of dry air at standard temperature and pressure.

Analyzing the Options

Let's examine each option based on the conversion and units:

• Option 1:

  $1.0\times10^{-3}$ grays

  This option is incorrect because the Gray (Gy) is the SI unit for absorbed dose, not exposure. The roentgen measures exposure.
• Option 2:

  $2.58\times10^{-4}$ coulombs per kilogram

  This option correctly states the conversion factor and uses the SI unit for radiation exposure (C/kg). This aligns with the definition of the roentgen in SI terms.
• Option 3:

  $1.6\times10^{-19}$ coulombs

  This option is incorrect. Coulombs (C) measure electric charge. The value $1.6\times10^{-19}$ C is the elementary charge (the magnitude of the charge of an electron or proton), which is unrelated to the definition of a roentgen.
• Option 4:

  $3.7\times10^{10}$ disintegrations per second

  This option is incorrect. Disintegrations per second (dps) measure radioactivity (activity), with the SI unit being the Becquerel (Bq). The value $3.7\times10^{10}$ Bq is equivalent to 1 Curie (Ci), another unit of activity. This is unrelated to radiation exposure measured in roentgens.

Conclusion

Based on the standard definition and conversion factors, one roentgen (R) is equivalent to $2.58 \times 10^{-4}$ C/kg$ in SI units.