Unrealistic radioactive decay

Hi,
today I am going to write about one of the problems that I had to solve for a physics seminar. The submissions for this series are already closed and you can look up the solutions so I know that I answered correctly to this very interesting problem.

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Imagine you have two types of particles, A and B. They are radioactive, meaning they keep falling apart but in a very peculiar way, A decays into B and B decays into A. This doesn’t happen in a real world because the particles decay into something smaller, they break up, but this is a hypothetical scenario very simplified, we do not care about what is happening on the inside. The question is, what is the ratio of the particles at any point in time?

Since the answer itself and the calculation are not trivial I will mainly try to make some facts about this problem obvious and then show the answer.

There is one part that I didn’t mention in the setup. Radioactive particles do decay but there is a very important value that characterizes how fast. It is either T (half-life) which tells you in what time will half of particles decay (if there is enough of them it will give the right results) or in other words when the time T passes one particle has 50% chance to decay. It seems that also decay constant, which I like better, is used which is basically half-life except the larger the value is, the faster the particles will decay.

The problematic part of this exercise is that when part of the A particles decay they will increase the pile of B particles which means that more particles will decay into A and so on, this is a cycle. To get to an important point it is good to try some simple case of such decay.

Let’s say we have 200 of A particles and 100 of B and half of both will decay in 1 hour. In 1 hour:

A=200-100+50=150
B=100-50+100=150

Next hour:

A=150-75+75=150
B=150-75+75=150

It is obvious that from now on the amount won’t change. This little experiment revealed something obvious, there, first of all, no particles get lost, there is always the same amount present: A+B=constant and with a bit more experimenting it would become more apparent that there is an equilibrium between A and B meaning there is always some amount of A that when it decays it will equalize the amount that decayed from B, this equilibrium will shift depending on the length of half-life or the decay constant. From these thought experiments that reveal the behavior of this problem, we need to use some math that I will not get into here to get the result that you can try to play around with in Desmos.

Dragallur

 

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How radioactivity was studied

Hi,
today I want to write about radioactivity. It is rather new concept which is not very surprising as the process of radioactive decay is not very visible and the effects (on health for example) are not so clearly connected since they usually have long time span. Probably largest work done on this topic was by Marie Curie and her husband Pierre.

This is how radium dials looked like, cute!

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Curie was from Poland. She had kind of difficult childhood since women were persecuted at that time in the east and it was hard for her to find place to study. Later on, she was able to move to Paris with her sister. There she met Pierre with whom she had two kids.

The first time she encountered with radioactivity was when she measured pitchblende [1] and uranium and how much radioactivity they  were “giving off”.

She expected that pure uranium would be much stronger but this was not what happened, what she found was exact opposite. Later on, thanks to this she found out two new elements: Polonium and Radium.

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At this time it was not yet known that you can get pretty easily cancer by being close to radioactive stuff. Curie and Pierre were buying tens of kilograms of pitchblende to do their research and prove those two new elements since lot of other scientists were kind of sceptic about it.

In November of 1898 they extracted compound that was 900x more radioactive than uranium, you can see where this was going.

In 1902 it was announced that one decigram of radium chloride was succesfully isolated.

Four years later Pierre died when wheel of carriege run over his skull, this was because of the effects of radioactivity, at this point he was not really able to use his hands, they were pretty much destroyed by the pitchblende and his whole health was in very bad state.

In 20′ it started to be more and more clear that there is something wrong with the stuff. There was actuall factory that painted dials with radium (not pure of course), this is because it glows nicely and everyone liked it. The brushes that were used for this had to be kept sharp and this was done by lips. For this work about 4,000 people were hired, the so called “Radium Girls” was a group of women that also painted for fun their nails, face and teeth, noone knows how many sacrifices this caused.

Dragallur

[1] Pitchblende is mineral that is radioactive since there is uranium and other heavy elements. Lot of miners in extreme conditions died because they were mining it.

All kinds of extreme nuclear explosions

Hi,
you surely remember Nagasaki and Hiroshima, probably not personally though at least from school.

Before and after at the place of explosion in Nagasaki

The amount of energy released by Little Boy (that is the bomb), was 63 tera Joules.

This is the same amount of  energy that would be released by annihilation 0.35 grams of any matter and antimatter.

This could sound like a small value but look again on the picture above, such an energy is able to wipe out entire city.

Now just take a moment to think how disastrous would be if we were able to create actual antimatter bombs. Remember your cat from last post? It weights roughly 4.5 kilograms. Now imagine that it would collide with the cat of your neighbor (accidentaly your neighbor somehow manages to hold antimatter cat). The amount of energy released would be about 1/100 of the energy used by USA every year.

Those are the cats that are flying towards each other creating huge explosion

This does not sound so impressive but now you must realise that the explosion would be equivalent to almost 26 Little Boys.

The graph that shows the power of explosions, Hiroshima is pretty small compared to largest nuclear test ever: Tzar Bomb.

Now there were other kinds of tests and the most violent, by SSSR was Tzar bomb.

 

Tzar bomb had the energy of 210 peta joules.

 

This is a lot. It had weight of 27,000 kilograms and its type was thermonuclear weapon.

It is estimated that the energy is 10 times the energy combined of all explosives in WWII.
It was actually planed to have it two times stronger but they realised that the airplane would not have a time to escape.

The fireball from the explosion did not touch a ground because of the shockwave.

The mushroom cloud was even 95 kilometers tall and at base 40 kilometers wide.

It was so powerful that it was possible to get 3rd level burns even 100 kilometers from the site of explosion.

Dragallur

Island of stability for dummies!

Hi,
island of stability is an area surrounded by lot of really fast decaying elements. Today I will write about island of stability which is on the other hand area with hypotheticly and relatively stable elements.

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By area I do not mean some place. It is rather area in periodic table of elements extended for various isotopes.

The more heavy nucleus of atom gets, the easier and better for him it is to decay, potentially killing everything around, or at least giving some nice brain tumors. But then at some point, some of the elements are smart enough to stay stable, like a boss. Those are the elements in island of stability, this island is not very big and we can just guess its highest peaks.

The elements are much more stable because of the shape of their nucleus. The problem is that the nucleus becomes a bit deformed, even elliptical.

Anyway there is this thing called “magic number” which is a number of protons or neutrons which can lead to good shape which is stable, this means round normally. Such numbers are for example 2,8,20,28… 126. There are few other hypothetical (196,236…), elements which live on this island should have some combination of these numbers which would make them much much more stable than the stuff around.

For example Ununoctium which is the last known element has half-life of only 890 microseconds.

The island should come in proton number of roughly 120 and little bit more.

Picture showing the island of stability (white circle). The most stable elements could last for longer than an year.

There is even hypothetical second island. It would have to be around element 164. Who knows how many more theoretical elements there are before we will simply not be able to stick all these protons and neutrons together (not that we are sticking them).

Dragallur

 

 

Conservation laws of physics

Hi,
today I want to talk about conservation laws of physics, at least some which I know about since there are just lot of them. Probably during your middle school/high school you have already encountered them. In chemistry when you have some reaction, for example:

Li + H2SO4—> Li(SO4)­ + H2

This could seem good but WordPress does not let me write upper index and (SO4) is -II which is by rule transfered to lithium —> Li2(SO4)

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If you ever saw this in school you may remember that now you need to add something since if we count there are two lithium atoms coming from the reaction while only one was there before, we have violated the law of conservation of matter, mass and probably many other laws.
It should go like this:

2Li + H2SO4—> Li2(SO4)­ + H2

Now there is equal amount of stuff on both sides of equation, only thing that happened was that those atoms changed their place.

Neutron decay

To see some laws of conservation we can write up the neutron decay during radioactive decay:

Neutron(0) —> Proton(+) + Electron (-) + anti-neutrino(0)

There is conservation of electric charge, we can test it: neutron has charge exactly 0. Proton has positive charge and electron has exactly the same charge but it is negative, when you put this together it is exactly zero. There is also anti-neutrino but it has charge zero too, so as you can see it does not violate the conservation of electric charge (I am not saying it is right, I am just saying that one law was not violated).

So as you can see from this rule, it may seem that this anti-neutrino thing was not necessary at all, but there are other laws of conservation which would be violated without this tiny particle.

Also here the conservation of quarks is not violated, there are three coming in and three coming out.

Leptons are particles that are not affected by strong nuclear force, those are electrons, mions, tauons and all types of neutrinos.

There is conservation of leptons, there is none coming in the reaction and two are coming out.. hmm
Electron is one lepton while anti-neutrino is anti-lepton which means that they will cancel out and there is zero of leptons in whole reaction, kind of.

So those are some basic laws of conservation but I read that there could be some special circumstances under which the amount of leptons or quarks could change.. look at the amount of matter in the Universe, it is much greater than the amount of anti-matter maybe this is such a case.

Still the most important law is the conservation of energy. Energy or mass since as Einstein’s equation says: E=mc2  —> mass is just different form of energy.

Neutron has little higher mass than proton, this little mass left is the mass which is than transferred to create electron and anti-neutrino.

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At last I was very curious how does it work with photon.
Everyone knows that photon has 0 mass and that is why he is able to travel at the speed of light.

E=mc2
E=0*c2
E=0

What? So photon does not have energy or what?  (c2=E/m … c2=E/0 (Universe just exploded))

The problem here is that E=mc2 works only for objects that are not moving, that are on one place which photon is not.

The full equation goes like this:
P is the magnitude of the momentum of vector p.

Where ħ is the reduced Planck constant and k is the wave vector which is:
k=2π/λ

Where λ is the wavelength of photon!! Finally we got to something which is understandable for me.

Dragallur

PS: I tried to get to some normal value using wavelength of orange light but I was not able to get something normal so I will update with new post when I will know what I did wrong.

Pictures from Planck constant page and neutron decay page

How it started, featuring Big Bang!

Hi,
when you read the title of this post it is pretty clear that I am going to write about Big Bang, I already wrote about the ends of the Universe but it feels as lot of people are interested in the beginning and there are some misconceptions.
For example even the title is little bit wrong since you could assume from it that Big Bang was the start of everything..

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So I will try to explain Big Bang and what happened right after and I want to start with first big misconception.
People think that Big Bang was explosion, nope it was not. It is thought that Universe expanded into space but actually Universe is already everything and it kind of expands into itself, if it makes sense.

On the picture above you can see the example of expansion where space expanded not the things inside but the fabric itself. The space in the grid increased while nothing happened to the objects except that they are further apart. This is what is happening all the time and even if the Universe was infinite it could get bigger, kind of, because everything is going away from the rest of the stuff and NOTHING can be the center of the Universe. There was no explosion.
For the rest of the post I will follow the picture on the left.

On the bottom of the picture is the start of the big bang. This is outside of the graph because we are not able to investigate it using the laws we know now. This is until Planck time passed (10^-43 seconds). After Planck epoch which is big unknown, the time of grand unification came. This is time with extremely high energies involved and it is assumed that 3 fundamental forces are working as one at this time: electromagnetism, weak and strong nuclear force. This is extremely important but we are not able to reach such energies even in particle accelerators while it could help us a lot with Theory of Everything.

Few really really short moment later strong force separated and started to work alone. This took some really long time before all the forces separated to the state we know today. This is one picosecond after big bang. Then quarks became grouping together into hadrons. Those are particles with zero “color” charge like neutron or proton.
Some time later finally deuterium is created and through big bang nucleosynthesis some heavier elements like lithium, beryllium and helium too.

Then it takes really a long time before everything calms down so that first stars and then galaxies form.

Some time I will probably return to background radiation.

At the beginning I said that you can not really say that big bang was the start of everything since there are some theories like big bounce.

Dragallur

1st picture
2nd picture

Some elements of periodic table

Hi,
today I am writing from Brazil which is why I had this few day pause from writing. I have got and idea to write about some elements of periodic table so this post will rather be mess of some stuff I found over time, probably a bit related to astronomy.

First of all I will start with one thing that comes to my mind and that is Hydrogen and Helium. Only those two elements in astronomy count as something different than metal.

The reason for this is that astronomers wanted to make some difference between the most important elements in universe and the rest and the rest was almost all metal.

Iron will be the next stop for me. Iron is very special because it is the last element which can be created through thermonuclear fusion. Actually star can fuse iron but only to isotope 55 and then the reaction would take energy to fuse any higher so it is the ending point of stars life. Higher elements can be created in supernovas.

Now let me jump right on the end of periodic table. The last known element is Ununoctium. It has proton number 118. He is also the last known noble gas right after Radon but this element with many others is synthetic which means that you can not find him in the nature and is only made in lab.
Once I asked my chemistry teacher where will be next element since Ununoctium marks the end of another period.
Sadly I had to find out by myself. The next one of course will be right under Francium.
But what is more interesting is that element with 121 proton number will have another shell filled, now it will be G shell. This element would also be the first superactinide.

To read more on this topic check out:
Island of stability
Interactive periodic table

Dragallur