Constants and Reference Values

Catalogs the universal physical constants and reference material-property values most used in physics.

Conceptual context

Physics is not just a collection of laws: it is a system of quantitative relationships in which every number carries a precise physical meaning. $k$ such as the universal gravitational constant G, Coulomb's constant k_e, and Planck's constant h are not mere numerical fillers: they are the bridge between a physical law and the numerical result of a calculation. Without knowing their exact values and $u$, any quantitative prediction lacks practical validity. $p_{mat}$ complete the picture: they characterize how a specific material responds to a given physical situation.

🟢 Essential level

Imagine you want to calculate how strongly the Earth attracts the Moon. Newton's law tells you the force depends on the masses and the distance, but you need a number that sets the scale of the gravitational interaction: that is the $k$ G. Without that value, the formula is just a proportion without units or real magnitude.

The same applies to electricity: Coulomb's law needs k_e to tell you how many newtons a pair of coulombs separated by one meter produce. In quantum physics, Planck's constant h fixes how much energy each photon carries.

$p_{mat}$ work differently: the density of copper, the specific heat of water, or the resistivity of aluminum depend on the material and conditions. They are not universal, but they are equally essential for calculating real phenomena.

Boltzmann's constant k_B, for example, connects the average thermal energy of a particle with the absolute temperature of the system.

🔵 Formal level

Basic formulas

The quantitative core of this leaf consists of three fundamental relations connecting $k$ to measurable physical quantities.

The electrostatic force between two point charges is given by:

Coulomb's Law

where $k_e = 8.988 \times 10^9 \text{ N m}^2 \text{ C}^{-2}$ is the $k$ that sets the scale of the electric interaction in vacuum. The result is the $F_e$ between $q_1$ and $q_2$, separated by $r$. The sign is determined by the product $q_1$*$q_2$: positive for equal charges (repulsion), negative for opposite charges (attraction).

The gravitational force between two point masses follows the same mathematical structure:

Newton's law of universal gravitation

with $G = 6.674 \times 10^{-11} \text{ N m}^2 \text{ kg}^{-2}$. This $k$ is twenty orders of magnitude smaller than k_e, which explains why gravity is negligible at atomic scales. The result is the $F_g$ between $m_1$ and $m_2$, separated by $r$; it is always attractive.

The energy of a photon depends on its frequency through:

Energy of a photon

where $h = 6.626 \times 10^{-34} \text{ J s}$ is Planck's $k$ and $c = 2.998 \times 10^8 \text{ m/s}$ is the speed of light in vacuum. Both are exact in the 2019 redefined SI. The result is the $E$ from its $f$; equivalently, it can be expressed through the $\lambda$.

Real student questions

Why does G have more uncertainty than h? Because measuring the gravitational force between laboratory objects is extremely difficult: it is of order 10^-9 N, easily masked by vibrations. The $u$ of h is zero since 2019 because the SI redefined the kilogram by fixing h exactly.

Does Coulomb's constant change in water? The value of the $k$ k_e never changes. What changes is the resulting force because the medium modifies the permittivity: F is equal to k_e * q1 * q2 / (epsilon_r * r^2). In water, epsilon_r ~ 80, so the force is 80 times smaller than in vacuum.

How many significant figures can I use in a result involving G? The relative $u$ of G is ~150 ppm, equivalent to ~6 significant figures. Therefore the result cannot have more than 6 significant figures even if the other data are more precise.

Final synthesis

$k$ set the numerical scale of each fundamental interaction and are identical throughout the universe. $p_{mat}$ characterize the response of specific materials under specific conditions. The $u$ of each value determines how many significant figures are valid in any physical calculation involving them.