Source / pinned edition
Bohr’s Model of the Hydrogen Atom
Source of package openstax.quantum · OpenStax University Physics, ch. 6 Photons and Matter Waves, module m58764
- work
- urn:openstax:clir:quantum#M58764
- number
- OpenStax University Physics, ch. 6 Photons and Matter Waves, module m58764
- kind
- urn:openstax:clir:quantum#treatise
m58764/index.cnxml at commit d0ed34a (main, 2026-06-11)
- edition
- urn:openstax:clir:quantum#M58764_MAIN
- language
- en
- officiality
- official
- materialisation
- PINNED_OFFICIAL_BYTES
- life cycle
- adopted: 2026-06-11
Publications
| URI | Type | documentHash | Retrieved |
|---|---|---|---|
| https://raw.githubusercontent.com/openstax/osbooks-university-physics-bundle/d0ed34a5851119a42e3d972dfc0ff49e4663977c/modules/m58764/index.cnxml | application/xml; charset=utf-8 | sha256:8d84f6d92317bf25194c8ac664270e5cb2891edbbf89b60a73ae37a88dae6447 | 2026-09-06T00:00:00Z |
Fragments — 5
module/m58764#fs-id1163713513317 · defn · referenced by: 2
en · official · sha256:793c3cec39ae29ebc22c8c6c9d2633350d27cffecffb08ce692933cdcd64312f
<definition id="fs-id1163713513317">
<term>emission spectrum</term>
<meaning id="fs-id1163713513322">wavelengths of emitted radiation by atoms and molecules</meaning>
</definition>Referencing norms: EmittedPhotonCarriesTheDifference, transition_between_levels
module/m58764#fs-id1163713513327 · defn · referenced by: 1
en · official · sha256:2f2a1e38fe8fa0a179358a0ca84a5fe81a50d2cb5f534f49f814641e86407d52
<definition id="fs-id1163713513327">
<term>energy spectrum of hydrogen</term>
<meaning id="fs-id1163713513332">set of allowed discrete energies of an electron in a hydrogen atom</meaning>
</definition>Referencing norms: is_a_hydrogen_atom
module/m58764#fs-id1163713430117 · defn
en · official · sha256:9fc1f30b9776c09f3e01255c2d963899d04bba353d7c2b3c191a4761ac558463
<definition id="fs-id1163713430117">
<term>ground state energy of the hydrogen atom</term>
<meaning id="fs-id1163713430122">energy of an electron in the first Bohr orbit of the hydrogen atom</meaning>
</definition>module/m58764#fs-id1163709831646 · defn · referenced by: 1
en · official · sha256:e2ace3a356601e4d1a0a3ba4c2f8f693ec1d4691af4d64f24b7eba1c4a81a1b9
<definition id="fs-id1163709831646">
<term>ionization energy</term>
<meaning id="fs-id1163709831651">energy needed to remove an electron from an atom</meaning>
</definition>Referencing norms: IonizationEnergyIsMinusTheGroundState
module/m58764#fs-id1163709757240 · section · referenced by: 2
en · official · sha256:f27ff883b74e9726f95d0d950b6a6215edf6314c05a40eea765e9d0e420c4245
<para id="fs-id1163709757240">Now we can see that the electron energies in the hydrogen atom are <emphasis effect="italics">quantized</emphasis> because they can have only discrete values of <m:math><m:mrow><m:mtext>−</m:mtext><m:msub><m:mi>E</m:mi><m:mn>0</m:mn></m:msub><m:mo>,</m:mo><m:mtext>−</m:mtext><m:mrow><m:mrow><m:msub><m:mi>E</m:mi><m:mn>0</m:mn></m:msub></m:mrow><m:mspace width="0.1em"/><m:mtext>/</m:mtext><m:mspace width="0.1em"/><m:mrow><m:mn>4</m:mn><m:mo>,</m:mo></m:mrow></m:mrow><m:mtext>−</m:mtext><m:mrow><m:mrow><m:msub><m:mi>E</m:mi><m:mn>0</m:mn></m:msub></m:mrow><m:mspace width="0.1em"/><m:mtext>/</m:mtext><m:mspace width="0.1em"/><m:mrow><m:mn>9</m:mn><m:mo>,</m:mo></m:mrow></m:mrow><m:mtext>−</m:mtext><m:mrow><m:mrow><m:msub><m:mi>E</m:mi><m:mn>0</m:mn></m:msub></m:mrow><m:mspace width="0.1em"/><m:mtext>/</m:mtext><m:mspace width="0.1em"/><m:mrow><m:mn>16</m:mn></m:mrow></m:mrow><m:mo>,</m:mo><m:mo>.</m:mo><m:mo>.</m:mo><m:mo>.</m:mo></m:mrow></m:math> given by <link target-id="fs-id1163713535556"/>, and no other energy values are allowed. This set of allowed electron energies is called the <term id="term-00028">energy spectrum of hydrogen</term> (<link target-id="CNX_UPhysics_39_04_H-energy"/>). The index <emphasis effect="italics">n</emphasis> that enumerates energy levels in Bohr’s model is called the energy <term id="term-00029">quantum number</term>. We identify the energy of the electron inside the hydrogen atom with the energy of the hydrogen atom. Note that the smallest value of energy is obtained for <m:math><m:mrow><m:mi>n</m:mi><m:mo>=</m:mo><m:mn>1</m:mn><m:mo>,</m:mo></m:mrow></m:math> so the hydrogen atom cannot have energy smaller than that. This smallest value of the electron energy in the hydrogen atom is called the <term id="term-00030">ground state energy of the hydrogen atom</term> and its value is</para>Referencing norms: HydrogenLevelFallsAsOneOverNSquared, HydrogenLevelOffTheSpectrumIsRefuted
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