Half life period is the time in which half of the atoms of a radioactive substances get disintegrated.For instance if I take 100 atoms of radium ,in 1600 yrs half of them (50)will undergo disintegration . What about another 50.Why they do not undergo the process of disintegration?How it is decided that which 50% will disintegrate?

>>What about another 50.Why they do not undergo the process of disintegration?

They will eventually.

>>How it is decided that which 50% will disintegrate?

Completely random.

See, what is happening here is that the radio active element is unstable. And by the laws of physics (Quantum mechanics) there is a probability at any given time that a particular element will break up. That probabilty is the same for each of the elements (as long as they have the same # of neutrons.)

So, in a given period of time, the probability for a single element is
p delta T. Now, there are so many elements that you will be close (percentage wise) to a certain percentage of all elements breaking up. But we cannot say which ones.

So, we have Delta Elements = p * # of elements * delta T.

or dElements/dt = - p or

# of elements = Elements (time = 0) * exp(-pt)
The remaining 50 atoms are still disintegrating. They will reduce down to 25 atoms of radium in another 1600 years. Then in another 1600 years, you will be left with 12.5 atoms. ETC. The remaining atoms don't just stop disentigrating after a single half-life, they keep going until all have been disentigrated.
Good question..no: really, it is. I'd say research into random physics of "chaos theory" might give clues into either the answers you seek.or pose even more questions for answers in this area.
Half life is about radioactive decay. This means that the atoms do not disinergrate but rather that particles are emitted (eg alpha or beta particles) that reduce some of the radioactive substance to a more stable product (although sometimes the product may be more radioactive and quickly decays into something else). Alpha radiation is when a helium nucleus is emitted to reduce the Ar (relative atomic mass) by 4 and the atomic number by 2, producing a different element. Beta decay is the emission of a beta particle (equivalent to an electron) thereby reducing the atomic number by one but not affecting the Ar.

e.g. 263Sg (atomic no 106) turns into 259Rf (atomic no 104) + 4He (atomic no 2) by alpha radiation.

The rate at which this decay happens is what dictates the "radioactivity" of the element and rate of decay is exponential.
radioactive disintegration is a continous process of autodisintigration.if half amount decays in 1600 years then half of remaining half would also decays in 1600years......,le... initial amount=A. then after one half life, it would be A/2. THEN A/4, THEN A/8 AND SO ON

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