A freshly prepared radioactive source of half-life 2 hours emits radiation of intensity which is 64 times the permissible safe level. The minimum time after which it would be possible to work safely with this source is?

Goldenman34

2 years ago

Try this:

1. Define variables:
- I_0: Initial intensity of radiation (64 times permissible level)
- I_safe: Permissible safe level of radiation
- t: Time elapsed (what we need to find)
- T_half: Half-life of the radioactive source (2 hours)

2. Exponential decay relationship:
The intensity of radioactive materials decays exponentially over time. We can use the following equation to model this relationship:

I(t) = I_0 * (1/2)^(t / T_half)

where:
- I(t) is the intensity of radiation at time t
- I_0 is the initial intensity of radiation
- t is the elapsed time
- T_half is the half-life of the radioactive source

3. Relate initial intensity and safe level:
We are given that the initial intensity (I_0) is 64 times the safe level (I_safe). We can express this mathematically:

I_0 = 64 * I_safe

4. Safety condition:
For it to be safe to work with the source, the final intensity (I(t)) must be equal to or less than the safe level (I_safe).

I(t) = 6 * T_half

Plugging in the actual half-life (T_half = 2 hours):

t >= 6 * 2 hours

t >= 12 hours

So it will take at least 12 hours after the initial preparation for the radioactive source to become safe to work with, given the permissible safe level and the source's half-life.