Help with Math!: #1) 2 days (1 half-life = 8 h.) #2) 300 years (1 half-life = 5 years)?

Answer 1

Ok. Let's do the math.

#1 2 days if the half-life is 8 hours

There are 48 hours in 2 days. That's 6*8.
So, it halved 6 times.
That's 1/2 * 1/2 * 1/2 * 1/2 * 1/2 * 1/2 = (1 /2)^6= 1 / 64
So, if you had 64 grams of material, there would be 1 gram left after 8 days, for example. 64 gram * 1/64 = 1 gram

#2 300 years when half-life is 5 years

300 / 5 = 60, which means it was halved 60 times.
1/2 * 1/2 * 1/2 * (fifty-seven more times) = (1/2)^60 =
= 8.67362*10^(-19)
For example, a mole of an element is 6.0221415×10^23 atoms of that element. If that element had a half-life of 5 years, then after 300 years, there would be about 522,000 atoms left.

Answer 2

1.
2 days
1/2 life = 8 hours
2 days / 8 hours = 6 (since there is 24 hours per day)
this means there will be (1/2)^6 left of the original amount

2.
300 years
1/2 life = 5 years
300/5 = 60
this means that after 300 years, there will be (1/2)^60 left of the original amount

Answer 3

1.
M(8) = M0/2
M(16) = M(8)/2 = M0/4
M(24) = M(16)/2 = M0/8
M(8t) = M0/2^t
m = Mi*2^-t/h.l. = Mi*2^-(t/8 hr)
m(2 days) = Mi*2^-((2 da)(24 hr/da)/8 hr)
m(2 days) = Mi*2^-6
m(2 days) = Mi/64

2.
m = Mi/2^(300/5)
m = Mi/2^60
m = (8.6736*10-19)Mi

Answer 4

huh? you kinda have to type it more clearly