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Bohr Hydrogen Energy Levels & Mass-Energy Equivalence

玻尔氢原子能级跃迁与质能方程

En​=n2E1​​(E1​=−13.6 eV),hν=Em​−En​,ΔE=Δmc2

Theoretical Identity Description:

Bohr's quantization condition for atomic transitions: emitted/absorbed photon energy equals the difference between orbital energy states. Mass defect Δm yields binding energy ΔE.

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Rigorous Derivation Tree

2 Logical Steps
Step 1check_circleValid Deduction
En​=n2E1​​(E1​=−13.6 eV),hν=Em​−En​,ΔE=Δmc2

Foundational identity statement defined under standard mathematical conditions.

Step 2check_circleValid Deduction
hν=Em​−En​,ΔE=Δmc2

Targeted algebraic evaluation and parameter substitution.

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CSCA Exam Triggers & Traps

High-Yield Exam Focus
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Use for hydrogen spectrum series, nuclear fission/fusion binding energy, and radioactive decay equations.

errorCommon Examination Pitfalls

A group of hydrogen atoms at level n emits up to C(n,2) = n(n-1)/2 spectral lines, whereas a SINGLE atom emits at most (n - 1) lines.

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Related Formulas in Modern Physics

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Bohr Hydrogen Energy Levels & Mass-Energy Equivalence
玻尔氢原子能级跃迁与质能方程

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