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# K-Ar dating calculation

Working through a calculation for K-Ar dating (good to have some prior experience with e and logarithms). Created by Sal Khan.

## Want to join the conversation?

• In the last few video's Sal has done a wonderful job explaining how Carbon 14 is formed but I am left wondering, how does Potassium-40 form, and if it is not formed on Earth does that mean there might be a time when we could no longer use Potassium-40 to date rocks?
• All 40K is primordial, so it has been produced during the supernova that created our solar system. Since that time (4.55 Ga) it has gone through several half-lifes (1.25 Ga), so now only about 1/14 of the original 40K is still left. This is where most of the Ar in our atmosphere comes from.
• Is volcanic rock called obsidian?

Long answer: Obsidian is one of the many rocks hardened lava can form.
• Wait, around , did Sal accidentally divide by -ln 2 instead of (+)ln 2? Or did I miss something?
• Yes he did divide by - ln 2. It seems like when he solved for k eariler in the video, Sal took into account the minus sign -k= ln (1/2) /1.25*10^9 ,so when it is simplified k = ln (2) / 12.5*10^9, but since "e" is to the power of "-k" (minus K) to use the "simplified "version he would need use the minus sign so -k = - ln (2) / 12.5*10^9, or he could have used the other expression -k= ln (1/2) /1.25*10^9. I hope this helps but I think I might have just muddied the waters further.
• In figuring out the initial total mass of K-40, shouldn't he also take into account the Ca-40 decay product?

Something like Kf = 1 mg +(Ar/.11)+(Ca-40/.89)
• We don't have a good way to determine how much Ca-40 the sample started with though, so we can't use it to determine which portion formed from K-40 decay. We only use Ar because the material should have been nearly completely free of Ar when it first solidified. So, any Ar found will be from K-40 decay.
• i thought this was science not math
• Math is used as an precise way of describing relationships between things in science. There is no better method for describing many things in science than mathematics.
• Where did the power of 9 come from?
• Going off of the previous answer, I think he was using scientific notation. Sal's made some videos on it, but its basic use is to make very large or very small numbers easier to use and comprehend quickly. (For example, 1*10^27 is easier to read than 1,000,000,000,000,000,000,000,000,000.) I hope this helps!
• I'm very confused.... is there any other way to figure this out? In the video before this one said that the fish fossil is in between 2 layers with the ages of 100 million years and 150 million years. Technically shouldn't it be 125 million years? Because 125 million is between 100 million and 150 million. What is the natural log? What is with the e and the -kt? Please explain and tell me if I'm wrong! Thank you for the help!! :)
• I'm going to choose a number between 100 and 150, and you have to guess what it is. Do you guess 125? Well, you are wrong, because I chose 108.

Sal has videos on natural logarithm.