142
votes
Accepted
Why doesn't a nucleus-like body made up of just neutrons exist?
The reason for this is that unlike the electrostatic force the nuclear force depends on how the spins of the two particles are aligned. The force is stronger when the spins are in the same direction ...
- 363k
77
votes
Accepted
Can there be an atomic nucleus where there are more protons than neutrons?
What you are looking for is isotopes with neutron–proton ratio N/Z less than 1. You can find these isotopes, for example, in this list from Wikipedia. As you can see, you are looking for members of ...
62
votes
Can light become a satellite of a black hole?
No, light cannot form stable, bound orbits around a black hole.
The possible trajectories of light around a Schwarzschild black hole are conveniently parameterised in terms of the "impact ...
- 136k
44
votes
Can there be an atomic nucleus where there are more protons than neutrons?
According to Wikipedia:
Other than protium (ordinary hydrogen), helium-3 is the only stable isotope of any element with more protons than neutrons.
- 49.4k
43
votes
Accepted
Why is helium-4 the only nuclide with a negative nucleon binding energy?
Helium-4 won't accept a neutron to form helium-5, and it won't accept a proton to form lithium-5: both of those isotopes have ground states which decay by alpha-nucleon fragmentation. But you are ...
rob♦
- 94.2k
42
votes
Accepted
Why certain rotations are unstable? (Euler Equations)
There is another nice way of seeing this mathematically. It is not too hard to show that in the body frame, there are two conserved quantities: the square of the angular momentum vector
$$
L^2 = L_1^...
- 51.6k
39
votes
Why do unstable nuclei form?
There are a few different ways that unstable nuclei are produced:
Nuclear fusion is quite a common way to produce unstable nuclei in nature. At high enough energies, stable nuclei can fuse together ...
- 35.8k
37
votes
Accepted
What does it mean when an isotope is stable?
Does stable mean that an isotope has a very long half life... or does it mean that fissure is theoretically not possible, or does it mean that the isotope has a very long half life, but the exact ...
- 51.6k
29
votes
Why does chaos preclude exact solutions?
You are right about this wording being sloppy. A chaotic system is a deterministic system whose solutions at late times are exponentially sensitive to early times. Nothing about this definition ...
- 8,900
26
votes
Accepted
How can I prove that a state of equilibrium is unstable?
In the centre of a bowl there is equilibrium.
Put a ping pong ball in it. If this ball is ever shaken slightly away from equilibrium, it will immediately roll back. A "shake-proof" equilibrium is ...
- 52.3k
23
votes
Are elements above 137 possible?
Empirically, nuclei composed from magic numbers of nucleons ( either proton number or neutron number, separately) which follows Otto Haxel's relation
$$a(n) = \frac{n(n^2 + 5)}{3} \tag 1$$
Starting ...
- 14.9k
22
votes
Are elements above 137 possible?
For a point nucleus with $Z \gt 1/\alpha$ the Dirac equation has no ground state solution for a single electron, that is a +(Z-1) ion. Itzykson and Zuber describe this catastrophe on page 75. For a ...
- 26.6k
17
votes
Why do unstable nuclei form?
There's no fundamental principle that makes unstable states unable to exist. It's just that by being unstable, they won't exist for a long time. For example, take a cone. You could sit the cone on a ...
- 22.1k
16
votes
Accepted
Are electroweak particles stable?
It's isn't terribly meaningful to say that Photons made of the electromagnetic force or that the W and Z bosons made of the weak force, though it's certainly true that these particles are the gauge ...
- 363k
16
votes
Why do elements, as they have more protons, need a higher amount of neutrons to stabilise them?
The nuclear force only acts between nearest neighbors to hold them together- but the electrostatic force driving them apart has infinite range, so any one proton in the nucleus feels the repulsion of ...
- 97.8k
15
votes
Why are $L_4$ and $L_5$ lagrangian points stable?
As others have commented, including OP, the effective potential (consisting of gravity & the centrifugal potential)
$$V~=~ -\frac{Gm_1}{|z_1|}
- \frac{Gm_2}{|z_2|}
-\frac{\Omega^2 |z|^2}{2} \tag{...
- 213k
15
votes
Why certain rotations are unstable? (Euler Equations)
There's an alternative to @MichaelSeifert method which uses angular momentum and moments of inertia: it is to deal with the vector $\vec\omega$ directly as we are interested in the evolution of this ...
- 47.8k
13
votes
Objects falling from table
If the centre of gravity of the object is vertically above the edge of the table then the object is in equilibrium. However, this equilibrium position is unstable (like a pencil balanced on its point) ...
- 60.3k
13
votes
Why is the number of isotopes of an element bounded?
I think this is a good question -- after all, if there's no extra Coulomb repulsion penalty for adding more neutrons, unlike for protons, why can't nuclei have lots of neutrons?
One model for the ...
- 2,456
13
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Why is there a sudden drop-off in half-life of isotopes at around 130 neutrons? Is there a name for this?
The instability is actually centred on N=128 neutrons, not N=130, and is caused by N=126 being a neutron magic number. Isotopes with magic numbers of neutrons have greater binding energies than those ...
- 13.2k
13
votes
Is there proof for: "Elements heavier than iron will decay to iron by processes such as fission and alpha emission"?
Nuclear decay is a quantum process and as long as their exists a final state with lower energy than the initial state, and electric charge, baryon and lepton number are conserved, a nucleus will ...
- 13.2k
11
votes
Crystals and Earnshaw's theorem
As mentioned by @tippy2tina, the Pauli exclusion principle (a quantum phenomenon) is one reason, and the other is the discrete nature of electron states in a potential well (another quantum phenomenon)...
- 12.2k
11
votes
Can perfectly stable orbits exist in GR?
In the literature, the orbits you are looking for a called “floating orbits”. Floating orbits are not possible in plain GR (See e.g. 1302.1016).
- 12.9k
10
votes
Why doesn't a bike/bicycle fall if going with a high speed?
I am sorry, but the way this topic is treated in the discussion below is a complete and embarrassing mess. Some of the answers below are complete nonsense, and the by far most competent answer (by ...
- 3,783
10
votes
Accepted
Why do (short) strands of hair keep a horizontal position while falling?
I'm not a falling hair expert, but this behavior sounds reasonable enough so I'll take a crack at it.
The hair is short enough, thin enough, and light enough that it reaches its terminal velocity ...
- 4,916
10
votes
Accepted
What is the state of the equilibrium for a second derivative equal to zero?
Consider the following potentials:
\begin{align} U(x) &= x^4 \\ U(x) &= x^6 - x^4 \\ U(x) &= x^4 + x^3 \end{align}
All three of these potentials have an equilibrium point at $x = 0$. ...
- 6,515
10
votes
Why do unstable nuclei form?
It seems that you're thinking that unstable nuclei must be formed by a special process that other nuclei are not. This is incorrect: they are formed by exactly the same processes as stable nuclei, and ...
- 20.8k
10
votes
Can there be an atomic nucleus where there are more protons than neutrons?
For an atomic nucleus to be stable, the repulsive force between protons must be less than the binding energy.
This doesn't really make any sense. You can't compare binding energy to repulsive force. ...
- 6,389
10
votes
What does it mean when an isotope is stable?
This half-life of $1.8\cdot 10^{22}$ years was actually measured.
At first glance it seems impossible to measure such a long half-life.
But let's go through the numbers to see that is indeed scarcely ...
- 41k
10
votes
How can two black holes merge without violating No Hair?
The no-hair theorem refers to stationary black hole solutions to the Einstein equations. If the black holes in question are undergoing dynamics, then the no-hair theorem doesn't apply. Specifically, ...
- 71.3k
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