Question

the half life of radioactive radium is 1620 years. what percent of a present amount of radioactive radium will remain after 100 years

Answer 1

To calculate the remaining percent of radium after 100 years, use the formula for exponential decay with its half-life of 1620 years. After applying this formula, it shows that slightly less than 100% of the original sample will remain.

The question involves radioactive decay and the concept of half-life, which is a fundamental aspect of nuclear chemistry. To determine what percent of a sample of radioactive radium will remain after 100 years when the half-life is 1620 years, we use the formula for exponential decay:

N(t) = N0 · (1/2)^(t/T)

where:

• N(t) is the remaining quantity of the substance after time t,
• N0 is the initial quantity,
• t is the time that has elapsed,
• T is the half-life of the substance.

Applying this formula to the given problem:

N(t) = 100% · (1/2)^(100/1620)

We can calculate the fraction of the remaining radium and then convert it into percent.

So, a very small fraction of decay will have occurred after 100 years due to the long half-life of radium, so slightly less than 100% of the radium would remain.

Answer 2

About 95.81%

Step-by-step explanation:

Often quantities grow or decay proportional to their size like decay of radioactive material

In those cases, we use the next formula:

`y=Ce^(kt)`

where:

y: The amount of radioactive radium

t: Time

k: The decay constant

C: The initial amount of radium

"the half life of radioactive radium" -
`(1)/(2)C`

`y=Ce^(kt)\\\\(1)/(2) C=Ce^(k*1620)\\\\(1)/(2) =e^(1620k)\\\\ln((1)/(2))=ln(e^(1620k))\\\\ln((1)/(2)) = 1620k\:ln(e)\\\\1620k=ln((1)/(2))\\\\k=(ln((1)/(2)))/(1620)\\ \\k=-4.2786862997527488* 10^(-4)\\`

What percent of a present amount of radioactive radium will remain after 100 years (t)?

`y=Ce^(kt)\\\\y=Ce^{-4.2786862997527488*10^(-4)*100}\\\\y=0.9581155781885929\:C\\\\\%=y*100\\\%=0.9581155781885929\:C*100\\\%=95.81155781885929`