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## Class 12 Physics (India)

### Course: Class 12 Physics (India)>Unit 13

Lesson 3: Half life and decay rate

# Half-life and carbon dating

Carbon dating is a real-life example of a first-order reaction. This video explains half-life in the context of radioactive decay. Created by Sal Khan.

## Want to join the conversation?

• If all C-14 will eventually become nitrogen, then why is there C-14 at the first place? and why does it still exist? • Can hydrogen with an atomic mass of 1 decay? • I have read several estimates for the "half-life" of a proton. The longest I read was at least 10 to the 109th years. I would like to verify an "at least this long" and a competent source for the half-life of a proton, Thank you! • To the best of my knowledge, proton decay (not meaning β⁺) is entirely hypothetical and has never been observed despite multiple efforts to do so. I would not put much credence in any such conjecture. It might be the case that the 13.8 billion or so years the universe has existed in its current form is just far too short of a time for protons to decay. Or, maybe they never decay. Who knows. But, if it happens at all, it would appear to be an exceedingly rare event -- perhaps even more rare than Big Bang events.
• At roughly or so, Sal mentions that after the half-life is up, we're left with half and half (half old element/half new element). He then implies that in another set number of years (the half-life), the remaining concentration of the original element will have a probability of "changing" via beta decay, ending in 75% of the original concentration being the "new" element by the end of this 2nd half-life.

My question: If this is all based on probabilities, why do we press the figurative "reset" button once the half-life number of years has been achieved? In other words, don't the remaining original elements have an even more likely chance of decaying sooner than later, because they've already been waiting for their turn to decay (for the original amount of years it took to achieve a half-life)?? I'm envisioning a bell-curve here, where the chance at decaying becomes exponential as one (an element) misses the "average" time-line of a decay...

Hope this makes sense...thanks! • It is possible to determine the probability that a single atomic nucleus will "survive" during a given interval. This probability amounts to 50% for one half-life. In an interval twice as long (2 T) the nucleus survives only with a 25% probability (half of 50%), in an interval of three half-life periods (3 T) only with 12.5% (half of 25%), and so on.
You can't, however, predict the time at which a given atomic nucleus will decay. For example, even if the probability of a decay within the next second is 99%, it is nevertheless possible (but improbable) that the nucleus will decay only after millions of years.
It’s like flipping a coin. If you flip “heads” ten times in a row, what are the chances that the next flip will be “heads”. You might say, “I’ve flipped ten heads in a row. The next one is much more likely to come up “tails”. Nevertheless, your chances of flipping heads are the same as before: 1 out of 2.
Some nuclei are much luckier at flipping the coin than others. They keep flipping until they get “tails”; then they decay.
• I am learning about half--lifes and this video explains pretty well but I am still confused on the overall picture, could someone please explain this to me in a easier sense? It would really help me on the half-life quiz we're about to have. • How is the half-life of Carbon-14 calculated at 5,740 years when no one has lived that long to actually measure the amount left? What is the technique that actually establishes the half-life time duration? • The half-life of a radioactive element is the time it takes before half of the atoms in a sample of the element have decayed.

If you know how many atoms you have in a sample, and you measure how many of them decay per second, it is easy to figure out how long you would have to wait before half of all the atoms have decayed. You do not have to measure until half the atoms actually have decayed, but the tradition is that we use the half-life as a measure of how quickly a radioactive element decays.
• After a half-life, half of 10g of C-14 turns into N-14 like Sal shown above and we have 5g of C-14 and 5g of N-14. So after another half-life, half of 5g of C-14 turns into N-14, but what will the 5g of N-14 turns into? • How do they turn into nitrogen? • When an atom loses or gains protons in its' nucleus, it changes what type of element it is.
In this case in particular of beta decay, a neutron becomes a proton in the carbon atom and ejects an electron. The new atom has 1 proton more (the number of neutrons does not determine the type of atom) and thus become the element with one more proton than carbon --> which is nitrogen.
So in a similar way, for alpha decay, the nucleus ejects two proton and two neutrons as an alpha particle, then the nucleus has changed its' composition and due to the loss of protons, the atom will be the element with two fewer protons.
• At the video states that indiviudal C14 atoms don't know when to change, and that it's ultimately up to random chance when a certain atom decays. How then are we able to accurately determine a specific rate of decay for a large mass of atoms if each atom's chance of decay is random? • How long does it take them to actually change the nucleus composition?
Is it a gradual change over 5740 years or an instantaneous change after each half-life? 