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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

Ever wonder why certain ancient artifacts can be dated back thousands of years? Or why we need to replace some medical radioactive tracers after a while? The answer lies in the concept of half-life. Let&#39;s dive into the fun, mysterious world of decaying atoms.

<ul>
	<li>Definition: The time taken for half the nuclei in a radioactive sample to decay.</li>
	<li>Cool Fact: After one half-life, the activity of a radioactive sample drops to half of its initial value!</li>
	<li>Mathematical Relation: T1​/2 ​= \(\frac {In(2)}{ λ}\)​ where &lambda; is the decay constant.</li>
</ul>

<ul>
	<li>Defines how quickly a substance decays.</li>
	<li>Higher &lambda; = Faster decay.</li>
	<li>Real-World Example: Imagine two ice creams melting under the sun. One melts super fast while the other takes its sweet time. The &quot;melting rate&quot; of each ice cream can be compared to the decay constant of radioactive materials.</li>
</ul>

P-32 has a half-life of 14.3 days, let&#39;s decode its mysteries.

&nbsp;

Decay Constant Calculation: Given, T1​/2​ = 14.3 days (converted to seconds = 14.3 &times; 24 &times; 3600 s)

&nbsp;

Using our formula, \(λ = \frac {In(2)}{T_1/2}\)

&nbsp;

So, &lambda; = 5.61 &times; 10&minus;7s&minus;1

&nbsp;

🤓 Fun Fact: This tiny number means P-32 doesn&#39;t decay super fast. But give it a few weeks, and you&#39;ll definitely notice!

&nbsp;

Initial Activity

<ul>
	<li>Convert mass to number of nuclei</li>
	<li>Given molar mass of P-32 = 32 gmol&minus;1 N0​=\(\frac {2.0 × 10^{-3}}{32× 6.02 × 10^{23}}\) = 3.8&times;1019&nbsp;nuclei.</li>
	<li>Calculate activity: A0 ​= &lambda; &times; N0​= 2.1&times;1013Bq.</li>
</ul>

🌟 Real-World Connection: Bq (Becquerel) is the unit of activity. Imagine each Bq as one &quot;pop&quot; every second. So, 2.1 x 1013 Bq is A LOT of pops!

&nbsp;

Remaining Mass after 30 Days

<ul>
	<li>Using decay formula</li>
</ul>

&nbsp;Mass remaining =&nbsp; e&minus;5.61 &times; 10&minus;7&nbsp;&times; 30 &times; 24 &times; 3600 = 0.47mg.

<ul>
	<li>Alternatively, by half-lives: 30 days = 2.10 half-lives. Remaining mass = 2.0&times;(0.5)2.10&nbsp;= 0.47mg.</li>
</ul>

🍕 Food for Thought: Both methods yield the same result. It&#39;s like measuring a pizza slice either with a ruler or by eating half of it twice and seeing how much is left!

Understanding half-life and decay constant is crucial in many fields, from archeology to medicine. With these tools, we can unlock the secrets of the past and predict the future behavior of radioactive materials. So, the next time you hear about carbon dating or medical isotopes, give a nod to these powerful concepts! 📚🔍🎉

Theme E - Nuclear & Quantum Physics

Decoding Half-Life: Dive Into Phosphorus-32 Decay Analysis

Table of content

Real-World Concept 🌍

Half-life (T₁/₂) 🚀

Decay Constant (λ) 🕰️

Unlock the Full Content!

Theme E - Nuclear & Quantum Physics

Decoding Half-Life: Dive Into Phosphorus-32 Decay Analysis

Table of content

Real-World Concept 🌍

Half-life (T₁/₂) 🚀

Decay Constant (λ) 🕰️

Unlock the Full Content!