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Microscope

Theme E - Nuclear & Quantum Physics

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Rocket

Theme A - Space, Time & Motion

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Thermometer

Theme B - The Particulate Nature Of Matter

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Water Wave

Theme C - Wave Behaviour 

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Magnifying Glass Tilted Right

Theme D - Fields

Imagine you have a heap of candy, and every hour, half of that candy magically disappears. The time it takes for half the candy to disappear is its &quot;half-life&quot;. Now, replace candy with radioactive atoms, and you get the idea! 😁

Long Half-lives: Imagine a magical candy that takes a year for just half of it to disappear! This is what long half-lives are like. It&#39;s when the half-life is much longer than the time we measure.

For long half-lives

<ul>
	<li>Direct Method: Use the equation A = &lambda;N</li>
	<li>Substitution &amp; Rearrangement Method: T1/2​=&nbsp;\(\frac {0.693}{A} × N\)</li>
</ul>

Glossary

<ul>
	<li>A: Activity of the sample (kinda like how active or hyper the candy is in disappearing!)</li>
	<li>&lambda; (lambda): Decay constant (how fast our atoms are decaying)</li>
	<li>N: Total number of atoms</li>
</ul>

Imagine Thorium-232 (Th-232) as a mystical element from a fantasy movie. This cool guy decays to radium-228, leaving behind a magic trail!

&nbsp;

Problem: You have a 5.0g sample of Th-232.

<ul>
	<li>Find the number of Th-232 nuclei.
	<ul>
		<li>Given the sample has an activity of 2.0 x 104 Bq, determine:</li>
		<li>Decay constant</li>
		<li>&nbsp;Half-life of Th-232</li>
	</ul>
	</li>
</ul>

Solution:

<ul>
	<li>To find the number of nuclei, you use the molar mass (it&#39;s like asking, &quot;how much does each atom weigh in grams?&quot;). For Th-232, it&#39;s 232 g/mol.&nbsp;</li>
	<li>\(N = {5.0}{232} × 6.02 × 10^{23} = 1.3 × 10^{22}\)</li>
	<li>To find the decay constant,&lambda;&nbsp;\(λ = \frac AN = \frac {2.0 × 10^{4}}{1.3 × 10^{22}} \)&nbsp;= 4.5 &times; 10{17}s</li>
	<li>To find the half-life</li>
</ul>

&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp;&nbsp;\(T_{1/2} = \frac {0.693}{λ} = \frac {0.693}{1.5 × 10^{-18}} \)&nbsp;= 4.5 &times; 10{17}s

Woah! That&#39;s 1.4 x 1010 years! To give you a perspective, if Th-232 started decaying from the time the very first dinosaurs appeared, it would still be decaying now!

Thorium-232 is like the granddaddy of isotopes! It&#39;s a primordial nuclide, meaning it&#39;s been around since before Earth was even formed. Imagine Th-232 chilling with a cup of tea, watching planets form. Cool, right?

&nbsp;

Remember: Half-lives might sound complex, but they&#39;re just about understanding how long something takes to halve itself. So, the next time you see candy disappearing from your stash, maybe it&#39;s just experiencing its half-life (or maybe someone&#39;s eating it 😉).

Theme E - Nuclear & Quantum Physics

Unveiling The Secrets: Long Half-Lives & Thorium-232 Explained

Table of content

What are half-lives?

Types of Half-lives

How to determine half-lives?

Unlock the Full Content!

Theme E - Nuclear & Quantum Physics

Unveiling The Secrets: Long Half-Lives & Thorium-232 Explained

Table of content

What are half-lives?

Types of Half-lives

How to determine half-lives?

Unlock the Full Content!