If the radiological half life of a material is 31 minutes, and you have 77 grams
now, how much did you have 55 minutes ago?
k = 0.0.693/t1/2
k = 0.693/31 = 0.0224 min^-1
ln(No/N) = kt
No = unknown
N = 77
k = from above.
t = 55 min
look at the intro to nuclear physics (2500U) tutorial notes (tut 6 i think)
To find out how much of the material you had 55 minutes ago, you need to consider the decay of the material over time based on its radiological half-life.
The radiological half-life is the time it takes for half of the material to decay. In this case, the half-life is given as 31 minutes.
To calculate the remaining amount of material after a certain time has passed, you can use the formula:
Remaining amount = Initial amount * (1/2)^(time / half-life)
In this case, the initial amount is 77 grams and the time is 55 minutes.
Plugging in these values:
Remaining amount = 77 * (1/2)^(55 / 31)
Calculating this:
Remaining amount ā 77 * (0.5)^(1.774)
Remaining amount ā 77 * 0.593
Remaining amount ā 45.681 grams
Therefore, you would have had approximately 45.681 grams of the material 55 minutes ago.