Before we proceed, know that a "__continuous spectrum__" is a rainbow-like spectrum that occurs when a prism * diffracts* ("splits") white light.

**The Atomic Emission Spectrum for Hydrogen**

When a hydrogen atom absorbs energy (h*v*), its single electron becomes __excited__ and moves to a higher energy state.

When the excited electron later falls back or "relaxes" back down to its __ground state__, the electron releases the absorbed energy by * emitting* light of various wavelengths.

➞ what results is the __line emission spectrum for hydrogen__.

Here's a * visual* of 3 types of relaxations of an electron from 3 different excited states (n = 3, n = 4, n = 5), to the n = 2 state:

In 1913, Neils Bohr proposed that the 3 relaxations and the energy levels (n) correspond to an electron's circular orbit.

Additionally, these 3 relaxations correspond to 3 of the 4 lines in the __line spectrum for hydrogen__:

**Emission Spectrum for Hydrogen**

## Bohr Model for Hydrogen

In Bohr's circular orbit model, the electron cannot be found "just anywhere," but instead * only* in those n = 1, 2, 3, ... energy-level orbits.

➞ mathematically, these __quantized energy levels__ available to hydrogen's electron are given by the Rydberg equation...

**The Rydberg Equation**

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*ex:* Calculate the energy required to

__excite__the hydrogen electron from level n = 1 to level n = 2. Also, calculate the wavelength of light that must be

__absorbed__by a hydrogen atom in its ground state to reach this excited state.

_________

**answer:**Now, calculating the wavelength (λ) gives us 1.216 x 10^{-7} m, as shown here:

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* NOTE* - In the last example, the first equation used is often re-written as:

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*ex:* Calculate the energy required to

__remove__the electron from a hydrogen atom in its ground state.

_________

**answer:**so, **n _{i} = 1** (ground state)

**n**(entirely removed)

_{f}= ∞we have...

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That's all for this post, but we're just getting started with **SECTION 7 - The Quantum Mechanical View of the Atom.**

We'll continue next time with Quantum Numbers and Polyelectronic Atoms.