# Is it correct to say energy occurs in quanta of magnitude $\frac{h}{2\pi}$?

I read this thing in a book called Concise Inorganic Chemistry By JD Lee.It says-

According to Planck's quantum theory,energy is not continuous but is discrete.This means that energy occurs in 'packets' called quanta, of magnitude $\frac{h}{2\pi}$.The energy of an electron in an orbit, ie. its angular momentum $mvr$, must be eqaul to a whole number $n$ of quanta.

Now,I knew that $E$ is multiple of $h\nu$.But why does this book say $\frac{h}{2\pi}$?Is this correct?

• That is not correct. And energy is not angular momentum. Those errors make the entire book suspect. Jul 28 '17 at 18:15
• @garyp Yeah...But the book seemed quite standard... because the 'About the author' part says-"Senior Lecturer in Inorganic Chemistry at Loughborough University"... Jul 28 '17 at 18:17
• That is the reduced Planck constant, also known as hbar. It crops up as much as h itself, and if we could go back in time,we would probably use it rather than h
– user163104
Jul 28 '17 at 18:17
• $h\nu$ = $\hbar \omega$. Most equations are easier in $\omega$... Jul 28 '17 at 18:18
• Despite the author's credentials, he is wrong. Where were the editors? Jul 28 '17 at 18:18

This is a gross and incorrect generalization of a thing that is true in a limited sense.

It is true that bound quantum systems exhibit discrete eigenenergies.

It is true that for systems with a harmonic potential those discrete energies are separated by a fixed and constant amount of energy $h\nu = \hbar \omega$ where $\nu$ ($\omega$) is the frequency (angular frequency) of the system (harmonic potentials also have the property that this frequency is the same for all bound states).

It is not, however, true that all systems are bound, nor that all systems interact with harmonic potentials, nor that all harmonic systems have a unit angular frequency.

So

• Some systems are free and exhibit continuous spectra.
• Some bound systems are non-harmonic and exhibit non-constant spacing between discrete levels.
• Some harmonic systems have different step sizes.

No. The statement is nonsensical because $h/(2\pi)$ does not have units of energy - it has units of energy times time. It makes no sense for energy to come in units of something that isn't an energy.

Also, energy does not come in little units of anything. Physics is Lorentz-invariant. This means that if you have a photon of some energy $E$, you can shift into another reference frame and give the photon any energy you want. All energies are allowed. The book is wrong.

Regarding orbitals, the energy of an electron in a Hydrogen-like atom (only one electron) in SI units is

$$E_n = \frac{Z^2me^4}{8 n^2 h^2\epsilon_0^2}$$

where $Z$ is the atomic number, $m$ the electron mass, $e$ the electron charge, $h$ Planck's constant, and $\epsilon_0$ the permittivity of free space. As you can see, the energy does not come in units of $h/(2\pi)$, and this is only the simplest case; it ignores multiple electrons and other effects such as magnetism.

Also, angular momentum and energy are not the same thing, as the passage you quoted implies.

It appears the author simply used the word "energy" where they should have used the words "angular momentum".

In the Bohr model, angular momentum was hypothesized to come only in units of $h/(2\pi)$. This is not exactly the entire story, see this link on Wikipedia for more.