# 香蕉等效劑量

1香蕉等效劑量=0.0778微西弗。計算的依據主要是由於香蕉含有大量的元素，天然鉀當中約有百万分之117(0.0117%)的天然放射性的同位素鉀40。鉀40由於半衰期長達12億5千萬年（地球壽命為45億年）。每克天然钾的放射性活度，等于其中40K的原子数量除以40K原子以秒计量的平均寿命。每克天然钾中40K的原子数量是阿伏加德罗常数 6.022×1023除以天然钾的原子量39.0983克/摩尔再乘以40K的丰度0.000117，结果为1.80×1018每克。 对于指数衰减，平均寿命等于半衰期(3.94 × 1016秒)除以2的自然对数，结果为5.684×1016[1]因此每1克天然鉀中，放射性活度約31貝克勒。而1根香蕉中，平均而言約含有0.5克的天然鉀，[2]所以每根香蕉約含有放射性活度15.5貝克勒的放射性鉀40。依據美國環境保護署提供的轉換因數，每貝克的鉀40平均對每個成年人在50年期间造成的等效劑量为5.02納西弗。所以，1根香蕉的等效劑量=(15.5貝克勒)(5.02納西弗/貝克勒)=0.0778微西弗。1根香蕉中包含约15克碳中的碳-14(14C)提供了3-5次贝塔衰变每秒。

1根香蕉的辐射剂量，相当于每日的天然本底辐射的百分之一。即100根香蕉等效剂量。核电站对周边环境的最大允许辐射暴露是每年2500根香蕉等效剂量(250 μSv)。胸部CT扫描是7万根香蕉等效剂量(7 mSv)。致死剂量是3千5百万根香蕉等效剂量(3500 mSv)。距离1979年三里岛核事故10英里的人承受了800根香蕉等效剂量。[7]

## 参考文献

1. ^ Bin Samat, Supian; Green, Stuart; Beddoe, Alun H. The 40K activity of one gram of potassium. Physics in Medicine and Biology. 1997, 42 (2): 407. Bibcode:1997PMB....42..407S. doi:10.1088/0031-9155/42/2/012.
2. ^ Bananas & Potassium. [2011-07-28]. （原始内容存档于2011-08-14）. ...the average banana contains about 422 mg of potassium...
3. ^ U. S. Environmental Protection Agency (1999), Federal Guidance Report 13 页面存档备份，存于互联网档案馆, page 16: "For example, the ingestion coefficient risk for 40K would not be appropriate for an application to ingestion of 40K in conjunction with an elevated intake of natural potassiumm. This is because the biokinetic model for potassium used in this document represents the relatively slow removal of potassium (biological half-time 30 days) that is estimated to occur for typical intakes of potassium, whereas an elevated intake of potassium would result in excretion of a nearly equal mass of natural potassium, and hence of 40K, over a short period."
4. ^ Eisenbud, Merril; Gesell, Thomas F. Environmental radioactivity: from natural, industrial, and military sources. Academic Press. 1997: 171–172. ISBN 978-0-12-235154-9. It is important to recognize that the potassium content of the body is under strict homeostatic control and is not influenced by variations in environmental levels. For this reason, the dose from 40K in the body is constant.