A one for one emission would seem to be a lot of gamma radiation with 37,000 disintegrations per uCi.
I have to relocate some reference that I found earlier but exposure from gamma radiation from smoke detectors was considered minimal.
The last reference has a formula for calculating dose from radioactivity:
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"An empirical rule which may also be used is
6 x Ci x n x E = R/hr @ 1 foot,
where
Ci = source strength in curies.
E = energy of the emitted photons in MeV.
n = fraction of decays resulting in photons with an energy of E.
It should be noted that this formula and the gamma constants are for exposure rates from gamma rays and x-rays only."
***********************************************************************************************************************************************
Ci = .9E-6 Ci, E = .0597 MeV
Furthermore R (Roentgens) = .86 Rad = .86 rem. (ref. #3) and the equation becomes:
6 x Ci x n x E= .86 x rem/hr @ 1 ft.
Substituting, 3.75E-7 x n = rem/hr@1ft. or 3.75E-4 x n = mrem/hr@1ft. and
n = mrem/hr/3.75E-4 = 2.67E3 x mrem/hr@1ft
Now for the hard part. We have an number for the annual exposure in a typical home with an ionization type smoke detector of .008 mrem The inverse square law applies to radiation so we need to make an assumption as to the distance from the source. Let's say 10 ft. also, we need to estimate the number of hours/yr in proximity of the source. Let's say 2000. This will make the exposure 4E-4mrem/hr@1ft. Substituting in the equation, n = 2.67E3 x 4E-4 = 1.068. While the assumptions are just a wag, it implies that there is one 59,7 KeV x-ray photon emitted for each alpha particle.
I have to relocate some reference that I found earlier but exposure from gamma radiation from smoke detectors was considered minimal.
Calculate Your Radiation Dose | US EPA
This page provides a general tool to calculate an estimate of your annual radiation dose from sources the public may encounter.
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Radiation Absorbed Dose Rate, Total Ionizing Radiation Dose Rate Converter • Radiation and Radiology • Compact Calculator • Online Unit Converters
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The last reference has a formula for calculating dose from radioactivity:
***********************************************************************************************************************************************
"An empirical rule which may also be used is
6 x Ci x n x E = R/hr @ 1 foot,
where
Ci = source strength in curies.
E = energy of the emitted photons in MeV.
n = fraction of decays resulting in photons with an energy of E.
It should be noted that this formula and the gamma constants are for exposure rates from gamma rays and x-rays only."
***********************************************************************************************************************************************
Ci = .9E-6 Ci, E = .0597 MeV
Furthermore R (Roentgens) = .86 Rad = .86 rem. (ref. #3) and the equation becomes:
6 x Ci x n x E= .86 x rem/hr @ 1 ft.
Substituting, 3.75E-7 x n = rem/hr@1ft. or 3.75E-4 x n = mrem/hr@1ft. and
n = mrem/hr/3.75E-4 = 2.67E3 x mrem/hr@1ft
Now for the hard part. We have an number for the annual exposure in a typical home with an ionization type smoke detector of .008 mrem The inverse square law applies to radiation so we need to make an assumption as to the distance from the source. Let's say 10 ft. also, we need to estimate the number of hours/yr in proximity of the source. Let's say 2000. This will make the exposure 4E-4mrem/hr@1ft. Substituting in the equation, n = 2.67E3 x 4E-4 = 1.068. While the assumptions are just a wag, it implies that there is one 59,7 KeV x-ray photon emitted for each alpha particle.