Category: Physics

Playing with Electron Configurations

I upgraded the table part of the Electron Configuration Interactive I used in the app I made for Practicing Writing out Electron Configurations. It’s now more interactive and embeddable.

Click on the green cell (in the 3d subshell) to start adding electrons. Clicking on the previous cell will remove electrons.

The full documentation is here.

No Such Thing as Dark Matter

We’ve not been able to detect dark matter yet. Natalie Wolchover explains summarizes theories that could explain the way the universe works without having dark matter.

Key to it is the Modified Newtonian Dynamics (MOND) equation to explain why the stars at the outer edges of galaxies are moving faster than Newton’s force law predicts they should be.

Velocities of stars further away from the center of the galactic disk (larger R) have a higher velocity (V) than predicted by Newtonian physics. Dark matter has been used to explain this discrepancy, but tweaking the physics equations could do so as well. Image from Wikipedia.

Newton’s Second Law, finds that the Force (F) acting on an object is equal its mass (m) multiplied by its acceleration (a).

F = m \cdot a

The MOND equation adjusts this by adding in another multiplication factor (μ)

F = \mu \cdot m \cdot a

μ is just really close to 1 under “normal” everyday conditions, but gets bigger when accelerations are really, really small. Based on the evidence so far an equation for μ may be:

\mu = \frac{a}{a_0} \frac{1}{\sqrt{1+\left(\frac{a}{a_0}\right)^2}}

where, a₀ is a really, really small acceleration.

Factoring this μ factor into the equation for the force due to gravity ( F_g ) changes it from:

F_g = G \frac{ m_1 \cdot m_2}{r^2}

into:

F_g = G \frac{(m_1 \cdot m_2)}{r^2} + \frac{\sqrt{G \cdot \m_1 \cdot m_2 \cdot a_0}}{r}

The key point is that in the first term, which is our standard version, the denominator is the radius squared (r^2) while the second term has a plain radius denominator (r).

This means as the distance between two objects gets larger, the first term decreases much faster and the second term becomes more important.

As a result, the gravitational pull between, say a star at the edge of a galaxy and the center of the galaxy, is not as small as the standard gravitational equation would predict it would be, and the stars a the edge of galaxies move faster than they would be predicted to be without the additional term.

References:

What is Dark Matter?

Adam Hadhazy, in Discover Magazine, summarizes the top candidates to explain dark matter and the experiments in progress to find them. These include, WIMPs (Weakly Interacting Massive Particles, Axions, Sterile Neutrinos, and SIMPs (Strongly Interacting Massive Particles.

Distortions in the shapes of galaxies caused by gravitational lensing. While gravitational lensing is caused by anything with gravity (this means normal matter as well) the lensing effect of dark matter is a key form of evidence for its presence. Image of the galaxy cluster Abell 2218 via Wikimedia Commons.

via Brian Resnick on Vox, who provides some very interesting historical context on the discovery of dark matter.

Logic Gates

Truth tables by Seth Abels.

Logic gates are the building blocks of computers. The gates in the figure above take one or two inputs (A and B) and give different results based on the type of gate. Note that the last row of gates are just the opposite of the gates in the row above (NAND gives the opposite output to AND).

As an example, two gates, an AND and an XOR, can be used to make a half-adder circuit

Half adder circuit

By feeding in the four different combinations of inputs for A and B ([0, 0], [1, 0], [0, 1], and [1, 1]) you can see how these two gates add the two numbers in binary.

Creating a truth table for the half adder.

I find this to be an excellent introduction to how computers work and why they’re in binary.