# Planck's constant

## Key Questions

Planck's constant is instrumental and an unavoidable constant which appears in quantum mechanics.

#### Explanation:

Even though it was first introduced in the Planck's law,

${u}_{l a m \mathrm{da}} d \left(l a m \mathrm{da}\right) = \frac{8 \pi h c}{l} a m {\mathrm{da}}^{5} \cdot \frac{\mathrm{dl} a m \mathrm{da}}{{e}^{\frac{h c}{l a m \mathrm{da} k T}} - 1}$

Where one quantum of radiation would have an energy, $E = \frac{h c}{l a m \mathrm{da}}$, the concept of quantized radiation was extended by Einstein, later by Bohr in their theories as a part of the old quantum theory.

Today almost all important relationships in quantum mechanics, contain Planck's constant (or the reduced Planck's constant $\frac{h}{2 \pi}$).

Examples would include,

1) de Broglie relation -
$l a m \mathrm{da} = \frac{h}{p}$

2) Schrodinger equation -

$\frac{i h}{2 \pi} \frac{\partial \psi}{\partial t} = - \frac{{h}^{2}}{8 {\pi}^{2} m} {\left(\nabla\right)}^{2} \psi + V \left(\vec{r} , t\right) \psi$

3) Commutator of $x$ and ${p}_{x}$ -

$\left[x , {p}_{x}\right] = \frac{i h}{2 \pi}$

And so on.

It is to quantum mechanics, what the constants ${\epsilon}_{0}$ and ${\mu}_{0}$ are to Electricity and Magnetism.

Planck's constant is $h \approx 6.63 \cdot {10}^{-} 34 \setminus \text{J"*"s}$.

#### Explanation:

Planck's constant, in science, is denoted by $h$, and is given the value of

$h \approx 6.63 \cdot {10}^{-} 34 \setminus \text{J"*"s}$

Note that $1 \setminus \text{J"=1 \ "N"*"m}$

$= 1 \setminus \text{kg"*"m/s"^2*"m}$

$= 1 \setminus {\text{kg"*"m"^2"/s}}^{2}$

And so, we can rewrite $h$ as

$h \approx 6.63 \cdot {10}^{-} 34 \setminus \text{kg"*"m"^2"/s"^2*"s}$

$= 6.63 \cdot {10}^{-} 34 \setminus {\text{kg"*"m"^2*"s}}^{-} 1$

This is one of the smallest constants in physics, and gives the relationship between a photon's energy and its frequency.