The Balmer series is characterized by the electron transitioning from n ¡Ý 3 to n = 2, where n refers to the radial quantum number or principal quantum number of the electron. The transitions are named sequentially by Greek letter: n = 3 to n = 2 is called H-¦Á, 4 to 2 is H-¦Â, 5 to 2 is H-¦Ã, and 6 to 2 is H-¦Ä. As the spectral lines associated with this series are located in the visible part of the electromagnetic spectrum, these lines are historically referred to as H-alpha, H-beta, H-gamma and H-delta where H is the element hydrogen.

Balmer Series (Second) (visible light) n=2 limit = 365 nm

n = 3, ¦Ë = 656.3 nm, ¦Á, color emitted: red
n = 4, ¦Ë = 486.1 nm, ¦Â, color emitted: bluegreen
n = 5, ¦Ë = 434.1 nm, ¦Ã, color emitted: violet
n = 6, ¦Ë = 410.2 nm, ¦Ä, color emitted: violet
Although physicists were aware of atomic emissions before 1885, they lacked a tool to accurately predict where the spectral lines should appear. The Balmer equation predicts the four visible absorption/emission lines of hydrogen with high accuracy. Balmer's equation led physicists to find the Lyman, Paschen, and Brackett series which predicted other absorption/emission lines found outside the visible spectrum.

The familiar red H-alpha line of hydrogen which is the transition from the shell n=3 to the Balmer series shell n=2 is one of the conspicuous colors of the universe contributing a bright red line to the spectra of star forming regions.

Later, it was discovered that when the spectral lines of the hydrogen spectrum are examined at very high resolution, they are found to be closely-spaced doublets. This splitting is called fine structure. It was also found that excited atoms could jump to the Balmer series n=2 from orbitals where n was greater than 6 emitting shades of violet.

[edit] Balmer's formula
Balmer noticed that a single number had a relation to every line in the hydrogen spectrum that was in the visible light region. That number was 364.56 nm. When...

...Fourier series
From Wikipedia, the free encyclopedia
Fourier transforms
Continuous Fourier transform
Fourier series
Discrete-time Fourier transform
Discrete Fourier transform
Fourier analysis
Related transforms
The first four partial sums of the Fourier series for a square wave
In mathematics, a Fourier series (English pronunciation: /ˈfɔərieɪ/) decomposes periodic functions or periodic signals into the sum of a (possibly...

...hp calculators
HP 50g Using Taylor Series
The menu LIMITS AND SERIES Practice using Taylor series
hp calculators HP 50g Using Taylor Series The menu LIMITS AND SERIES The menu LIMITS AND SERIES contains commands related to limits. To access it you press !Ö. You are presented then the calculus menu as a CHOOSE box:
Figure 1
Its second menu item is 2.LIMITS AND SERIES... You can use...

...Taylor series with two terms, y = 0.830.
When y = sin (5), y = -0.958. Using the Taylor series with two terms, y = - 15.8.
When y = cos (1), y = 0.540. Using the Taylor series with two terms, y= 0.500.
When y = cos (5), y = 0.284. Using the Taylor series with two terms, y = - 11.5.
By using the formula, Percentage Error =
Percentage Error for Taylor series with two terms =
= 1377.18 % ≈ 1380 %...

...Solution: Apply integral test: Z Z
ln R 1 X
R
2
1 p dx x (ln x) p=1 p 6= 1
let ln (x) = u then
ln 2
so that when p = 1 and p < 1 integral diverges by letting R ! 1, so does the series. When p > 1 then integral converges to ! 1 p 1 p 1 p (ln R) (ln 2) (ln 2) lim = , R!1 1 p 1 p 1 p so does the series. 2. (18 pts.) Find the in…nite sum 1 : n (n + 2) n=1 Solution: See that 1 1 = n (n + 2) n 1 n+2
1 X
8 R < ln ujln 2 ln 1 ln R du = 1 p : u p up 1...

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To stand out and become well known in the public is certainly not an easy thing to achieve. Someone must have the courage to sacrifice...

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3. Time series methods are based on the assumption that historical patterns of demand are a good indicator of future demand, and that over a period of time, demand can be charter in three different ways: as an underlying trend (flat, up , or down), as a circle (daily, weekly, seasonally , and so on), and as irregular fluctuations (peaks or valleys) over time.
4. Simulation methods are a combination of causal and time series...

...Fourier Series
Fourier series started life as a method to solve problems about the ﬂow of heat through ordinary materials. It has grown so far that if you search our library’s data base for the keyword “Fourier” you will ﬁnd 425 entries as of this date. It is a tool in abstract analysis and electromagnetism and statistics and radio communication and . . . . People have even tried to use it to analyze the stock market. (It didn’t help.) The representation of...