5-25 rad: No observable effects. 25-75 rad: Chromosomal aberrations and temporary depression of white blood cell levels in some individuals. No externally observable effects. 75-200 rad: Vomiting in 5 to 50% of exposed individuals within a few hours. Fatigue and loss of appetite. Moderate blood changes. Recovery within a few weeks. 200-600 rad: For doses over 300 rem, all exposed individuals will exhibit vomiting within 2 hours and loss of hair after 2 weeks. Severe blood changes with hemorrhage and increased susceptibility to infection, particularly at higher doses. Recovery from 1 to 12 months for individuals at the lower end of the dose range; only 20 percent survive at the upper end of the range. 600-1000 rad: Vomiting within 1 hour, sever blood changes, hemorrhage, infection, and loss of hair. From 80 to 100% of exposed individuals will succumb within 2 months; those who survive will be convalescent over a long period. Introduction to Nuclear Engineering (Lamarshe)
See the "history" page on my site for a description of the Army SL-1 that went critical in Idaho in the 60s. That's one I didn't learn about until recently, and apparently it was a pretty hot one too.
There is a common belief that 'going critical' is synonymous with a meltdown, or out-of-control chain reaction or manifold other bad things. This is, however, false.
A nuclear reactor is a device which creates chain reactions to amplify the effects of neutrons. The neutron multiplication factor describes whether the number of neutrons present in the core is increasing, decreasing, or remaining the same. Based upon this, the following are defined:
Subcritical: there are fewer neutrons in the current neutron generation than in the previous neutron generation, e.g. the neutron multiplication factor is less than one. Critical: there are exactly the same number of neutrons in the current neutron generation than in the previous neutron generation, e.g. the neutron multiplication factor is equal to one. Supercritical: there are more neutrons in the current neutron generation than in the previous neutron generation as a result of delayed neutrons only, e.g. the neutron multiplication factor is greater than one. Prompt Critical: there are more neutrons in the current neutron generation than in the previous neutron generation as a result of prompt neutrons alone, e.g. the neutron multiplication factor is equal to one plus the reciprocal of 1-beta, where beta is the fraction of neutrons which are delayed.
Therefore: 1) A reactor must be critical to maintain its power. 2) A reactor must be supercritical to increase in power. Criticality and supercriticality are normal states for a reactor. It's prompt criticality which is bad.
5 rem is the maximum allowable occupational total effective dose equivalent (10CFR20.1201). Assuming that you don't work in a nuclear plant or other facility licensed to use radioactive materials, then 10CFR20.1301 applies instead:
"... The total effective dose equivalent to individual members of the public from the licensed operation does not exceed 0.1 rem (1 mSv) in a year, exclusive of the dose contributions from background radiation, from any administration the individual has received, from exposure to individuals administered radioactive material and released under 35.75, from voluntary participation in medical research programs, and from the licensee's disposal of radioactive material into sanitary sewerage in accordance with 20.2003.... The dose in any unrestricted area from external sources, exclusive of the dose contributions from patients administered radioactive material and released in accordance with 35.75, does not exceed 0.002 rem (0.02 millisievert) in any one hour...."
These limits don't apply to radioactive trees, of course -- at least not these radioactive trees, since they don't arise from licensed activities.
Do note that dose as low as you postulate is unlikely to have harmful effects, particularly because the dose would be spread out over time. These are the effects from acute doses of radiation of varying intensities:
5-25 rad: No observable effects. 25-75 rad: Chromosomal aberrations and temporary depression of white blood cell levels in some individuals. No externally observable effects. 75-200 rad: Vomiting in 5 to 50% of exposed individuals within a few hours. Fatigue and loss of appetite. Moderate blood changes. Recovery within a few weeks. 200-600 rad: For doses over 300 rem, all exposed individuals will exhibit vomiting within 2 hours and loss of hair after 2 weeks. Severe blood changes with hemorrhage and increased susceptibility to infection, particularly at higher doses. Recovery from 1 to 12 months for individuals at the lower end of the dose range; only 20 percent survive at the upper end of the range. 600-1000 rad: Vomiting within 1 hour, sever blood changes, hemorrhage, infection, and loss of hair. From 80 to 100% of exposed individuals will succumb within 2 months; those who survive will be convalescent over a long period. from Introduction to Nuclear Engineering, Lamarshe
As you can see, a non-acute dose as low as would be expected from these trees really shouldn't harm anyone.
Alpha radiation is the least harmful type of radiation if it's outside of your body, since it is stopped by the layer of dead cells on your skin, but, taken internally, alpha emitters are the WORST type of radiation, since they deliver the most energy at once. If bananas actually emitted alphas, eating them would be quite bad for both you and the banana.
However, a quick glance at the Chart of the Nuclides shows that you're wrong about K-40's mode of decay:
Half life: 1.277E+9 years Mode of decay: Beta to Ca-40 - Branch ratio: 89.28 % - Decay energy: 1.311 MeV Mode of decay: Electron capture to Ar-40 - Branch ratio: 10.72 % - Decay energy: 1.505 MeV
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5-25 rad: No observable effects.
25-75 rad: Chromosomal aberrations and temporary depression of white blood cell levels in some individuals. No externally observable effects.
75-200 rad: Vomiting in 5 to 50% of exposed individuals within a few hours. Fatigue and loss of appetite. Moderate blood changes. Recovery within a few weeks.
200-600 rad: For doses over 300 rem, all exposed individuals will exhibit vomiting within 2 hours and loss of hair after 2 weeks. Severe blood changes with hemorrhage and increased susceptibility to infection, particularly at higher doses. Recovery from 1 to 12 months for individuals at the lower end of the dose range; only 20 percent survive at the upper end of the range.
600-1000 rad: Vomiting within 1 hour, sever blood changes, hemorrhage, infection, and loss of hair. From 80 to 100% of exposed individuals will succumb within 2 months; those who survive will be convalescent over a long period.
Introduction to Nuclear Engineering (Lamarshe)
There is a common belief that 'going critical' is synonymous with a meltdown, or out-of-control chain reaction or manifold other bad things. This is, however, false.
A nuclear reactor is a device which creates chain reactions to amplify the effects of neutrons. The neutron multiplication factor describes whether the number of neutrons present in the core is increasing, decreasing, or remaining the same. Based upon this, the following are defined:
Therefore: 1) A reactor must be critical to maintain its power. 2) A reactor must be supercritical to increase in power. Criticality and supercriticality are normal states for a reactor. It's prompt criticality which is bad.
5 rem is the maximum allowable occupational total effective dose equivalent (10CFR20.1201). Assuming that you don't work in a nuclear plant or other facility licensed to use radioactive materials, then 10CFR20.1301 applies instead:
These limits don't apply to radioactive trees, of course -- at least not these radioactive trees, since they don't arise from licensed activities.
Do note that dose as low as you postulate is unlikely to have harmful effects, particularly because the dose would be spread out over time. These are the effects from acute doses of radiation of varying intensities:
As you can see, a non-acute dose as low as would be expected from these trees really shouldn't harm anyone.
Alpha radiation is the least harmful type of radiation if it's outside of your body, since it is stopped by the layer of dead cells on your skin, but, taken internally, alpha emitters are the WORST type of radiation, since they deliver the most energy at once. If bananas actually emitted alphas, eating them would be quite bad for both you and the banana.
However, a quick glance at the Chart of the Nuclides shows that you're wrong about K-40's mode of decay:
Half life: 1.277E+9 years
Mode of decay: Beta to Ca-40
- Branch ratio: 89.28 %
- Decay energy: 1.311 MeV
Mode of decay: Electron capture to Ar-40
- Branch ratio: 10.72 %
- Decay energy: 1.505 MeV
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