The half-life of a radioactive substance is 15 hours. If at some instance, the sample has a mass of 512 g, calculate the time it will take \(\frac{7}{8}\) of the sample to decay

3my123

3 years ago

though i studied physics, yet i don't consider myself any special in physics, i prefer maths anyday.
my guess;
lets take N = 512g
remember for every 15hrs we have a half life of this radioactive substance or sample
15hr = N/2
15hr= 1/2 x N/2 = N/4
15hr = 1/2 x N/4 = N/8
from here we add up N/2 + N/4 + N/8 = 7/8N
recall N = 512
therefore,7/8N = 7/8 x 512g = 448g
also we add add up the time taken to achieve 7/8N. i.e, 15hr + 15hr+ 15hr = 45hrs
therefore, b4 7/8 of the sample of 512g mass which is 448g would decay, 45hrs would have elapsed or passed

Award0001

2 years ago

don't know how many of you have come across this formula but its super short and reliable
Nt/No = (1/2)^t/T
7/8 decayed meaning 1/8 still remains
1/8 = (1/2)^ t/15
but 1/8 = (1/2)^3

(1/2)^3 = (1/2)^t/15
cancel out (1/2)

3 = t/15
t = 15×3 = 45hrs

Zebrimin

1 year ago

i don't know how to solve it

upd8

2 years ago

It's common sense sha

Aiwansedoetionsa

3 years ago

15Hours is correct