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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 your favourite chocolate candy bar melting away on a hot summer day. Just as the chocolate will not disappear instantly, some atomic particles don&rsquo;t either! 🍫☀️

<ul>
	<li>The &#39;melt rate&#39; of our chocolate or the &#39;speed&#39; at which atoms disappear.</li>
	<li>For any atom, it&#39;s the probability (P) it&#39;ll decay in a tiny bit of time (&Delta;t). So, P = &lambda;&Delta;t.</li>
	<li>But be careful! This works only if &Delta;t is super tiny, like a chocolate crumb, compared to the atom&rsquo;s average lifetime.</li>
</ul>

FYI: This average lifetime isn&rsquo;t the half-life (the time it takes for half of something to disappear). So don&#39;t mix them up!

Worked Example 11 - The Mystery of Polonium-210 (Po-210)

<ul>
	<li>Initial activity: 2.3 &times; 108&nbsp;Bq (Imagine this as the brightness of 2.3 million light bulbs 💡)</li>
	<li>Decay constant: 5.8 &times; 10-8&nbsp;s-1&nbsp;(How fast they dim)</li>
</ul>

Finding Initial Mass

<ul>
	<li>\(A_o = λN_o → N_o = \frac {A_o}{λ} = 4.0 × 10^{15}\)&nbsp;nuclei.</li>
	<li>Convert nuclei to moles:&nbsp; N0 ​&divide; NA&nbsp; = 6.6 &times; 10-9&nbsp;mol.</li>
	<li>Initial mass = 6.6&times;10&minus;96.6&times;10&minus;9 mol &times; 210 g/mol = 1.4&micro;g (Lighter than a feather! 🪶)</li>
</ul>

Activity after 100 days

<ul>
	<li>A = A0​e&minus;&lambda;t&nbsp; = 2.3 &times; 108 &times; e &minus;5.8&times;10&minus;8&times; 8.64 &times; 106= 1.4 &times; 108&nbsp;Bq (Half as bright!)</li>
</ul>

Worked Example 12 - The Fading Fluorine-18 🎇

<ul>
	<li>Count rate decreases: 45 count s-1&nbsp;&rarr; 28 count s-1&nbsp;in 4500s.</li>
</ul>

To find decay constant

<ul>
	<li>Using the decay formula, 28 = 45e&minus;4500&lambda;.</li>
	<li>Taking natural logarithm, &lambda; = \(\frac {In45 - In28}{4500} = 1.1 × 10^{-4} s^{-1}.\)</li>
</ul>

Worked Example 13 - The Antique Cloth &amp; Its Secrets 🧣

<ul>
	<li>The cloth&#39;s carbon-14 to carbon-12 ratio: 70% of living matter.</li>
	<li>Carbon-14&rsquo;s half-life: 5700 years.</li>
</ul>

To find cloth&rsquo;s age

<ul>
	<li>Using decay formula: 0.70 =(0.5)n &rarr; n = \(\frac {Ino.7}{Ino.5} = 0.51.\)​&nbsp;</li>
	<li>Cloth&rsquo;s age: 0.51 &times; 5700&nbsp;= 2900 years (Imagine, this cloth might&#39;ve been worn by a Pharaoh or a warrior from the past! ⚔️👑)</li>
</ul>

<ul>
	<li>Radioactive dating using carbon-14 (from our cloth example) is used to date ancient artifacts and even mummies!</li>
	<li>Polonium-210 is super radioactive. In tiny amounts, it was even used to assassinate a former Russian spy!</li>
</ul>

Remember: This isn&#39;t magic; it&#39;s SCIENCE! 🎩🔬

&nbsp;

Happy studying! Stay curious, and always question the world around you! 🌏🔍

Understanding Decay Constant: The Nuance Of Nuclear Decay Probability

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Standard Level

Physics SL

Theme E - Nuclear & Quantum Physics

Understanding Decay Constant: The Nuance Of Nuclear Decay Probability

Table of content

Decay constant vs. Probability of decay

Decay Constant (λ)

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Theme E - Nuclear & Quantum Physics

Understanding Decay Constant: The Nuance Of Nuclear Decay Probability

Table of content

Decay constant vs. Probability of decay

Decay Constant (λ)

Unlock the Full Content!