# Question regarding half-life

1. Oct 28, 2004

### misogynisticfeminist

I've got a question regarding half-life. Half-life is the time taken when the mass or countrate emitted of a radioactive sample drops to half.

But if say, if a sample of 400 particular radioactive nuclides which go through radioactive decay. Won't the count rate reach 0 eventually, after decaying into a more stable state? (assuming no background count). Because if we plot a normal half-life curve, it would be exponential and would never reach 0 at all.

And if these particular nuclides emit gamma radiation, its mass wouldn't drop at all because the photons are massless, right?

Thanks.

Last edited: Oct 28, 2004
2. Oct 28, 2004

### da_willem

A 'normal half-life curve' is probably a plot of the expectation value of the number of particles in a certain state or a fraction. Nuclear decay is a probabilistic in nature, so all we can give is an expectation value or some probablility density.

If you use a half-life curve on your example. After some time the curve has decayed to almost zero indicating the chance to find a aprticle after that duration is very small, so probably there will be no particle left.

Note that a half life curve does not indicate the mass left, just the number of particles of a certain type. Or the mass of the particles of that certain type.

Note also that if a substance emits radiation it's mass decreases, because a photon has energy, wich also contributes to the mass of the object.

3. Oct 28, 2004

### NEOclassic

Hi miso,
IMO, whenever any nucleus emits a photonic particle, it is invariably coincidental to a simultaneous emission of a mass-bearing particle. E.g., a U-238 nucleus emits its most weakly attached alpha (of the 8 that it received when its parent, Pu-242, decayed), is accompanied by a ~45 KeV photon; the 4.190 MeV expulsion energy of the alpha (that is primarily controlled by electrostatic repulsion) is less than that which is available, 4.235MeV. Of course conservation of energy necessarily prevails. In order to cite details of photon emission that accompanies Beta (nucleus bound electron) emission, let me continue.
Let's talk about what happens to the new nucleus after U-238 loses its alpha. The reality is that it has become the nucleus of Thorium-234 that contains only 7 resident alphas; It is also quite nervous because the nucleus isn't happy because it has two too many neutrons. The only way to correct that problem is for a neutron to spontaneously emit an energetic electron. The Th-234 nucleus emits a beta thus becoming Protoactinium-234; the beta energy, depending on which one of 140 neutrons emits, is a spectrum of energies accompanied by a spectrum of photons. Typically, it might be suspected that high energy betas are accompanied by low energy photons; e.g., a 190 KeV beta coupled with a 29 KeV photon or a 100 KeV beta with a 91 KeV photon.
The Pa-234 decays in similar manner, to U-234; the betas are as much as 280 KeV and the gammas are as much as 1.68 MeV.
The U-234 is again an alpha emitter, and in similar manner repeats the alpha-beta-beta sequence until the nucleus has expelled all its available alphas thus becoming Pb-206. There are three other series that are represented by U-235, U-236 and U-233 as well as U-234 explained above. Thanks for your audience and your patience. Jim

4. Oct 29, 2004

### Mk

Since matter is but a highly concentrated form of energy, the missing mass has actually been converted to energy, in your case, a gamma ray. In spontaneous emission, the electron loses mass, as decending to a lower energy and the lost mass was actually mass converted to energy, and released as a gamma ray.

5. Nov 19, 2004

### transit442003

an exponential graph is just a prediction of what the mass would be after radioactive decay just bacause the graph does not reach zero doesn't mean that the particle won't become stable. it is just of those things that seem to happen, that is why we measure down to only one instead of zero.

day without sunshine.......................is well......................like..............night

Last edited: Nov 19, 2004