Final answer:
The radiation dosage in grays for a 61kg person exposed to a 3 Ci source of beta radiation is 8.88 Gy.
Step-by-step explanation:
In order to calculate the radiation dosage in grays for a 61kg person exposed to a 3 Ci source of beta radiation, we need to use the conversion factor between Ci and grays. One Ci (Curie) is equal to 3.7x10^10 disintegrations per second, and 1 gray (Gy) is defined as 1 joule of energy absorbed per kilogram of matter.
First, we need to find the number of disintegrations per second from a 3 Ci source, which is 3.7x10^10 x 3 = 1.11x10^11 disintegrations per second. Next, we can use the formula Gy = disintegrations per second x conversion factor to find the dosage in grays. The conversion factor from disintegrations per second to grays is 1.0x10^-10 Gy/disintegration.
So, the radiation dosage in grays for the 61kg person exposed for 8 seconds is:
Dosage (in grays) = disintegrations per second x conversion factor x exposure time
Dosage = (1.11x10^11 disintegrations/s) x (1.0x10^-10 Gy/disintegration) x (8 seconds) = 8.88 Gy