Problems in Natural Science

What if…?

What would happen, if electrons were bosons?

What would happen, if…?

Probably the whole physics were different. But we pretend that we can change one thing at a time, to understand it better.

Physics & Chemistry

Black Hole Earth

If all the thermal kinetic energy of atoms in the Earth would be applied as pressure on a tiny volume in the centre of our planet, would it be enough to turn the volume into a black hole?

If it would be enough, would the black hole suck in the rest of the Earth?

Hint: In order for the black hole to suck in the rest of the Earth, its Hawking radiation pressure should be less than the pressure of surrounding matter.

Acceleration Due to Gravity

In Star Wars, every planet has the same acceleration due to gravity as the Earth. Why?

How does the mass of a planet depend on its radius in that case? How to realise this relation in practice?

The answer.

The Charge Ratio of Electron & Proton

What would atoms be like, if the charge of proton were 1/2 or 1/3 of the charge of electron? Or if the proton charge were 2 or 3 times larger than the electron charge? Or the ratio of the electron and proton charges would be an irrational number?

How many chemical elements would there be?

Hint: If the difference of charges would come from changed proton charge, the ratio of the strong attracting force between nuclear particles to the electrostatic repulsive force between protons would change.

What would the periodic tabel be like?

Hint: It may be easier to enumerate chemical elements by the number of atomic electrons, not by the number of protons, or by nuclear charge.

Could there be molecules?

Hint: To bond with other atoms, an atom needs either unpaired electrons in the highest energy level, or that the difference between filled and free energy levels be small enough.

Would water, proteins and other compounds necessary for earthly life be possible?

Hint: For water to be liquid in the room temperature, there must be strong hydrogenic bonds between water molecules.

Could nuclear and thermonuclear reactions be used to generate energy?

Yukawa Hydrogen Atom

What would the energies & wave functions of s-states of the hydrogen atom be like, if instead of the Coulomb potential
$V = -e^{2} \frac{1}{r}$ there were the Yukawa potential $V = -e^{2} \frac{\exp (-m_{\gamma} c r/ℏ)}{r} = -e^{2} \frac{\exp (-K r)}{r}$ between proton and electron?

Note that $m_{\gamma}$ is photon mass, taken to be non-zero here.

Would the energies of states of hydrogen be lower or higher than in the case of a Coulomb potential?