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If someone would eat 5&nbspµg of the isotope of cesium ^{137}Cs, how long would it take for them to have only0,04 % of the original amount of this isotope? Assume that cesium ^{137}Cs has a half-life of 30,42 let and a biological half-life (the time it takes for half of the original amount of the material to leave the body) is approximately 5 days. Determine also, how many of the particles will have decayed in the body up till then.

The core of Bismuth ^{209}Bi sits impatiently at peace on the same spot. Suddenly it can't hold it any lonher and it falls apart. A thalium core ^{205}Tl remains and from it one can see an$αparticle$ shoot away. What is the speed of the $αparticle$, if the energy released during the decay becomes its kinetic energy? What is the velocity of the $αparticle$ in reality? Compare the results. The rest masses of the atoms are $M=m_{^{209}Bi}=208,980399u$, $M′=m_{^{205}Tl}=204,974428u$, $m=m_{^{4}He}=4,002602u$. Don't forget to check if one should use relativistic relations.

How much antimatter would we need to generate enough electricity for the Czech Republic for a year? We have enough matter and we assume that there would be no losses.

Imagine that no thermonuclear fusion occurs in stars and instead they run on nuclear fission. Estimate how long such a star would be able to shine if at the beginning of its life cycle it is composed of uranium 235, its mass and luminosity are both aproximately constant and are equal to the current values of the sun.

How many people per second can be killed by a nuclear reactor without any protective walls?

On the first day of winter old man Вова wanted to turn on his heater with input power 2 kW but found out that it was not working. Luckily, he realized that there was plenty of heat producing plutonium 237 in the warehouse where he was working. How much plutonium should he bring home in order to replace his old heater? You can assume that the plutonium is almost pure and that Вова has a lot of lead containers that can absorb all the energy radiating from the plutonium.

In 2000 a new nuclear waste repository was built. The first waste arrived and the government decided that every year the amount of newly delivered waste must be reduced by five percent. Assume for simplicity that the half-life of nuclear waste is 100 years (in reality it is much longer). Find out what year are the people in nearby villages going to receive the highest amount of radiation.

Luke has bought a Uranium atom and started to take away its electrons just for fun. After taking the $n-th$ one he surprisingly discovered that the mass of the atom had increased. What has inflicted this phenomena? Determine the value of $n$.

After Luke got bored with the ionization, he ordered more of the Uranium. The two perfect semi-spheres were delivered. Each semi-sphere has the mass $m$ ($m_{k}⁄2&ltm&ltm_{k}$, where $m_{k}$ is the critical mass). Luke has placed their flat sides opposite each other which started to bring them nearer. Calculate the distance $d$ at which the experiment was interrupted by the ignition of the chain reaction.