isotope A require 12h for its decay rate to fall to 1/64 of its intial value . isotope B has half-life = 1.5 half life of A
how long does it take for decay rate of B fall to 1/32 of its initial value ?
(1/2)^ 6 = 1/64
so we are talking six half lives for A is 12 hours
so one half life for A is 2 hours
Now I will read the problem :)
well half life of B is 3 hours
1/32 = 5 half lives
5 * 3 = 15 hours
Not hard, just keep your wits about you and think ! (and check my arithmetic :)
To find the time it takes for the decay rate of isotope B to fall to 1/32 of its initial value, let's follow these steps:
1. Determine the half-life of isotope A:
Since isotope A takes 12 hours for its decay rate to fall to 1/64 of its initial value, we can say that the half-life of isotope A is equal to 12 hours because a half-life is the time it takes for the decay rate to reduce by half.
2. Determine the half-life of isotope B:
The question states that isotope B has a half-life equal to 1.5 times the half-life of A. Therefore, the half-life of isotope B can be calculated by multiplying the half-life of isotope A by 1.5. Thus, the half-life of isotope B is 1.5 * 12 hours = 18 hours.
3. Calculate the time it takes for the decay rate of isotope B to fall to 1/32 of its initial value:
To find this time, we need to calculate how many half-lives it takes for the decay rate to reduce from its initial value to 1/32 of its initial value.
The decay rate of an isotope decreases by a factor of 2 with each half-life. So, if we want the decay rate of B to fall to 1/32 of its initial value, it means we need to have 5 half-lives because 2^5 = 32.
Since the half-life of B is 18 hours, multiplying it by the number of half-lives (5) will give us the total time:
Time = Half-life of B * Number of half-lives = 18 hours * 5 = 90 hours.
Therefore, it takes 90 hours for the decay rate of isotope B to fall to 1/32 of its initial value.