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State the Law of Radioactive decay?

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this may help you amir khan !
The law in simple words says that.. the rate of decay (how fast decay takes place) is directly proportional to number of atoms left.. which means.. if you have 1kg of radioactive sample.. then the rate is high.. but when it becomes 1/2 kg, the rate will be exactly half.. and so on!
What is the law's origin ? This law indicates that no of particles can never be zero. Why??

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Its a completely statistical process.. it depends on NOTHING else.. hence in his noble prize lecture Sir Becquerel called it a SPONTANEOUS PHENOMENON.. the no. of particles in an atom can never become zero because, as the no. of particles decreases, the rate of disintegration also decreases.. it simply keeps slowing down.. more and more.. in fact the radio active sample used by Ernst Rutherford for his infamous alpha scattering experiment which led him to the discovery of nucleus is STILL not completely decayed.. .. radioactivity truly an amazing phenomenon!
thank u
Note the origen is an observation and relationship between remaining nuclei after a time interval is the result of solving the differential equation which is a statement of that observation i.e., \[\frac{ dN}{ dt }= -\lambda N \] Where N is the number of nuclei at a given moment and Lambda is a constant characteristic of the decay. the minus sign because we know the rate is a decreasing quantity.
Actually because nuclei are discrete quantities they will eventually decay because when you get to one final nuclei and you will, it will decay. It may take a very long time though but not infinite.
Gleem.. not really.. it will not decay.. it ll take infinitely long time to really decay.. cause.. the rate of disintegration would have become so freaken small.. that when you come down to last nucleus.. it would never disintegrate!
Rate of decay is proportional to no. of nuclei present at that time. I will make it simple.Say 200 people are sitting in a boring lecture.When the professors turns to the board say 10 people from the backside jumped and ran away through the window.The professor will not notice that.As the time passes students escape from the class.And only 100 people remain.Now the prof will start to notice the attendance being reduced.When there is only a few students the chance of escaping gets near to rate is proportional to no. of nuclei at that time
thanks to all
mashy. When the final nuclei remains It will decays with the same time constant. A quantity of nuclei with a 1 year HL will be reduced to less than 10^-30 th of the original quantity after 100 years. Thus a mole of that substance 6x10^23 atoms will be reduced to less than i millionth of an ATOM by that time. meaning that will have probably decays 5 or more years ago...It is possible that it still might be around but unlikey. There is nothing to prevent it from decaying!!! the longer it lasts the more likely it will decay until it does.

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