Question

The Half-Life Of A Certain Isotope Is 2 Hours.If The Original Mass of Isotope was 12,000 Grams,How Many Grams Would Be Left After 1 Day?

Answer 1

Here it is. After 24 hours, the mass of the isotope will be `2.93` grams

Explanation:

At time zero you have 12,000 grams.

time 2 hrs, you will have `6000` grams
time 4 hours, you will have `3000` grams
time 6 hours, you will have `1500` grams
time 8 hours, you will have `750` grams
time 10 hours, you will have `375` grams
time 12 hours, you will have `187.5` grams
time 14 hours, you will have `93.75` grams
time 16 hours, you will have `46.875` grams
time 18 hours, you will have `23.438` grams
time 20 hours, you will have `11.719` grams
time 22 hours, you will have `5.859` grams
time 24 hours. you will have nearly `2.93` grams.

Answer 2

The mass is `=0.00293kg`

Explanation:

The equation for the radioactive decay is

`m(t)=m_0e^(-lambdat)`

The initial mass is `m_0=12kg`

The half life is `t_(1/2)=2h`

The radioactive constant is

`lambda=ln2/t_(1/2)=ln2/2`

Therefore,

`(m(t))/m_0=e^(-lambdat)`

`m_0/(m(t))=e^(lambdat)`

`lambdat=ln(m_0/(m(t)))`

The time is `t=24h`

Therefore,

`ln(m_0/(m(t)))=ln2/2*24=12ln2`

`m_0/(m(t))=e^(12ln2)=4096`

`m(t=24h)=12/4096=0.00293kg`

Answer 3

I get `2.93 \ "g"`.

Explanation:

From here, If `n` is the number of half-lives elapsed, then there will be `100/(2^n)%` of the substance left.

The half-life of this substance is `2` hours. One day is equal to `24` hours. So, after `1` day, the substance has elapsed `24/2=12` half-lives.

So, after `12` half-lives, their is only `100/(2^12)%=0.0244140625%` of the substance left.

Multiplying that by the original mass, there will only be

`0.0244140625%*12000 \ "g"=2.9296875 \ "g"~~2.93 \ "g"`

Therefore, there will only be `2.93` grams of the substance left after one day.