#### puremath

##### Active Member
The half-life of radium-226 is 1620 years.

A. How much of 2 g sample remains after 100 years?

B. Find the time required for 80% of the 2 g sample to decay?

#### MarkFL

##### La Villa Strangiato
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After working the first half-life problem, you should be able to do this one.

#### puremath

##### Active Member
After working the first half-life problem, you should be able to do this one.
Ok. I'll work on it.

#### puremath

##### Active Member
After working the first half-life problem, you should be able to do this one.
Is the formula needed k = [ln(1/2)]/(half-life)?

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#### puremath

##### Active Member
I will target this problem later as I have all day to do math. No place to go. NYC is currently in lock down mode.

#### puremath

##### Active Member
After working the first half-life problem, you should be able to do this one.

#### puremath

##### Active Member
After working the first half-life problem, you should be able to do this one.
For part B, must the first step be (0.80)(1.92 grams)?

#### MarkFL

##### La Villa Strangiato
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(a) $$\displaystyle A(100)=(2\text{ g})\left(\frac{1}{2}\right)^{\frac{100}{1620}}\approx1.91623115637718588\text{ g}$$

(b) $$\displaystyle \frac{1}{5}=\left(\frac{1}{2}\right)^{\frac{t}{1620}}$$

Solve for $$t$$.

puremath

#### puremath

##### Active Member
(a) $$\displaystyle A(100)=(2\text{ g})\left(\frac{1}{2}\right)^{\frac{100}{1620}}\approx1.91623115637718588\text{ g}$$

(b) $$\displaystyle \frac{1}{5}=\left(\frac{1}{2}\right)^{\frac{t}{1620}}$$

Solve for $$t$$.
Please, explain your set up for B. I will solve for t as we will continue with exponential growth and decay throughout the remainder of the week in addition to starting trigonometry tomorrow.

#### puremath

##### Active Member
(a) $$\displaystyle A(100)=(2\text{ g})\left(\frac{1}{2}\right)^{\frac{100}{1620}}\approx1.91623115637718588\text{ g}$$

(b) $$\displaystyle \frac{1}{5}=\left(\frac{1}{2}\right)^{\frac{t}{1620}}$$

Solve for $$t$$.
My answer for B makes no sense.

#### MarkFL

##### La Villa Strangiato
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$$\displaystyle 5=2^{\frac{t}{1620}}$$

$$\displaystyle t=1620\log_2(5)\approx3761.523513717527\quad\checkmark$$

puremath

#### puremath

##### Active Member
$$\displaystyle 5=2^{\frac{t}{1620}}$$

$$\displaystyle t=1620\log_2(5)\approx3761.523513717527\quad\checkmark$$
Wow! I got it right. What does the value for t mean here?

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puremath

#### puremath

##### Active Member
I know that t is time but time is 3761.52?

#### MarkFL

##### La Villa Strangiato
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The unit of time here is years. With a half life of 1620 years, we know 75% will be gone in 2 half lives, or 3240 years, and 87.5% will be gone after 3 half-lives or 4860 years. So it seems reasonable that it would take some 3800 years for 80% to decay.

puremath

#### puremath

##### Active Member
The unit of time here is years. With a half life of 1620 years, we know 75% will be gone in 2 half lives, or 3240 years, and 87.5% will be gone after 3 half-lives or 4860 years. So it seems reasonable that it would take some 3800 years for 80% to decay.
Wow! We will not be here for that.