Dear Antoine Nauleau ,

for a beginner it is a good approximation to use the KERMA as an estimation for the energy dose (KERMA = kinetic energy released in matter).

According to equation 2.4 of the book of Frank H. Attix

Book Introduction to Radiological Physics and Radiation Dosimetry

for monochromatic*) radiation the KERMA K is given by K= psi *(µen/rho) with

a) psi as the energy fluence calculated by the photon intensity I (as photon per area or photons per area and per time) times photon energy E: psi = I *E, and

b) (µen/rho) as the mass-energy transfer coefficient of the material; (µen/rho) depends on the type of material and on the photon energy E.

When looking at the units you see, that

a) the energy fluence psi is an energy per area or energy per area and per time, and

b) the (µen/rho) is an area per mass.

In consequence K is energy per mass or energy per mass and per time.

From basic knowledge on radiation safety you know, that the released energy per mass is the energy dose and the energy per mass and per time is the energy dose rate.

The unit of the energy dose is the Gy (Gray): 1Gy=1J/kg.

The unit of energy dose rate is Gy/s or Gy/min or Gy/h or Gy/a.

The radiation exposure you are interested in is the equivalent dose in Sv (Sievert) or equivalent dose rate in Sv/s or Sv/min or Sv/h or Sv/a

The relation to the energy dose (or dose rate) is given by:

equivalent dose [Sv] = energy dose [Gy]* WR with WR as the radiation weighting factor (formerly known as quality factor Q)

Please see for example:

https://en.wikipedia.org/wiki/Equivalent_dose

Fortunately the weighting factor WR (relative biological effectiveness) for gamma and x-rays is set to WR = 1.

So we have here: 1Gy will cause 1Sv.

I will intentionally not write an equation here !

In the above equation for K you need the mass-energy transfer coefficient for water. You find these energy dependent data here:

https://physics.nist.gov/PhysRefData/XrayMassCoef/ComTab/water.html.

So it is up to you now, to take an appropriate photon intensity I in photons per area or photons per area and per time (not keV/s as indicated in your question), to take the appropriate photon energy E and the appropriate (µen/rho) value and calculate the K. The most critical thing here is to handle all the different units and decimal powers in order to end up with J/kg for the Gy unit.

Good luck

*) for polychromatic radiation you have to perform an integral calculation according to equation 2,5 of the Attix book

Remark: I will send you the relevant pages of the Attix book via RG messenger

Dear Antoine Nauleau ,

for a beginner it is a good approximation to use the KERMA as an estimation for the energy dose (KERMA = kinetic energy released in matter).

According to equation 2.4 of the book of Frank H. Attix

Book Introduction to Radiological Physics and Radiation Dosimetry

for monochromatic*) radiation the KERMA K is given by K= psi *(µen/rho) with

a) psi as the energy fluence calculated by the photon intensity I (as photon per area or photons per area and per time) times photon energy E: psi = I *E, and

b) (µen/rho) as the mass-energy transfer coefficient of the material; (µen/rho) depends on the type of material and on the photon energy E.

When looking at the units you see, that

a) the energy fluence psi is an energy per area or energy per area and per time, and

b) the (µen/rho) is an area per mass.

In consequence K is energy per mass or energy per mass and per time.

From basic knowledge on radiation safety you know, that the released energy per mass is the energy dose and the energy per mass and per time is the energy dose rate.

The unit of the energy dose is the Gy (Gray): 1Gy=1J/kg.

The unit of energy dose rate is Gy/s or Gy/min or Gy/h or Gy/a.

The radiation exposure you are interested in is the equivalent dose in Sv (Sievert) or equivalent dose rate in Sv/s or Sv/min or Sv/h or Sv/a

The relation to the energy dose (or dose rate) is given by:

equivalent dose [Sv] = energy dose [Gy]* WR with WR as the radiation weighting factor (formerly known as quality factor Q)

Please see for example:

https://en.wikipedia.org/wiki/Equivalent_dose

Fortunately the weighting factor WR (relative biological effectiveness) for gamma and x-rays is set to WR = 1.

So we have here: 1Gy will cause 1Sv.

I will intentionally not write an equation here !

In the above equation for K you need the mass-energy transfer coefficient for water. You find these energy dependent data here:

https://physics.nist.gov/PhysRefData/XrayMassCoef/ComTab/water.html.

So it is up to you now, to take an appropriate photon intensity I in photons per area or photons per area and per time (not keV/s as indicated in your question), to take the appropriate photon energy E and the appropriate (µen/rho) value and calculate the K. The most critical thing here is to handle all the different units and decimal powers in order to end up with J/kg for the Gy unit.

Good luck

*) for polychromatic radiation you have to perform an integral calculation according to equation 2,5 of the Attix book

Remark: I will send you the relevant pages of the Attix book via RG messenger

the units keV/sec are meningles for what you are trying to establish

Article The radiation burden of radiological investigations