Balmer and Rydberg
Exploring Connections: Refining the Balmer Formula and Rydberg Constants
While examining timelines and numerical patterns inspired by the Book of Daniel in the Bible, I stumbled
upon an intriguing observation: the number 364.5, which emerged in my calculations, aligns closely with
the Balmer constant, a key value in atomic physics used to measure spectral lines in the hydrogen atom and
interpret "timelines" within the electromagnetic spectrum.
The Balmer Series: A Historical Insight
Johann Balmer, in 1885, discovered an empirical relationship in the hydrogen spectrum. He noted that a
single number—approximately 364.56 nanometers (nm)—correlated with every visible spectral line. This be-
came known as the Balmer series, one of six named series describing hydrogen’s spectral emissions, as
detailed in atomic physics. According to Wikipedia, “The Balmer series is calculated using the Balmer for-
mula,” providing a foundation for understanding light’s behavior at the atomic level.
A Curious Numerical Connection
Inspired by this, I explored a link between the biblical "1260 days" from Daniel and the Balmer constant.
Dividing 1260 by 364.5 yields approximately 3.456790123456790…, a repeating decimal notably missing the
digit 8. However, adjusting the divisor to 364.500117160… produces a "complete" sequence:
3.45678901234567890123456789…, now including the digit 8. This adjustment suggests a potentially more
precise Balmer constant. While 364.5 is a close approximation, 364.500117160… might reflect an exact value
worth further investigation.
Comparing Constants: Balmer and Rydberg
Today, the accepted values are:
Balmer Constant: 364.56 nm
Rydberg Constant: 1.097393690 × 10⁷ m⁻¹
My proposed adjustments are:
Adjusted Balmer Constant: 364.500117160…
Adjusted Rydberg Constant: 1.09739333725259647658240250480… (repeating pattern)
These refined numbers seem to harmonize in intriguing ways. For instance:
364.500117160… × 1.0973933372525… = 400 (exact)
364.56 × 1.097393690 = 400.0658436… (slightly off)
Mathematical Patterns and Geometric Insights
Further exploration reveals additional relationships:
364.500117160… ÷ 4 = 91.125029290…
Dividing successively by 2 down to 2.8476571653… and multiplying by 1.0973933372525… yields 3.125.
This 3.125 connects to pyramid geometry: 3125 units at 3.2π approximates the height to the pyramid’s tip, symbolizing the physical realm’s limit.
Other calculations:
364.5 × 4 ÷ 1.2 = 1215
364.56 × 4 ÷ 1.2 = 1215.2
364.500117160… × 4 ÷ 1.2 = 1215.00039053…, which, when scaled (÷ 1000 × 300), returns 364.500117160…
The ratio 1.2 appears significant, mirroring 2.1 (where 2.1 ÷ 1.2 = 1.75 × 4 = 7), possibly reflecting a geometric "diamond" shape in the spectrum’s structure.
Spectral Wavelengths with the Adjusted Constant
Using 364.500117160…, I calculated wavelengths across the visible and ultraviolet ranges:
Visible Range:
Red: (364.500… × 3²) ÷ (4 - 3²) = 656.1002 nm
Blue/Green: (364.500… × 4²) ÷ (4 - 4²) = 486.0001 nm
Violet: (364.500… × 5²) ÷ (4 - 5²) = 433.9287 nm
Violet: (364.500… × 6²) ÷ (4 - 6²) = 410.0626 nm
Ultraviolet Range:
7² = 396.9001 nm
8² = 388.8001 nm
9² = 383.4351 nm
Up to 21² = 404.8981150…, which simplifies back to 364.500117160…
These align closely with observed hydrogen spectral lines, suggesting the adjusted constant may enhance
precision.
Electromagnetic Spectrum and Number Patterns
The electromagnetic spectrum, when viewed mathematically, appears segmented into units of 37
(e.g., 0.37, 37), expanding symmetrically from a center point. For example:
1.11 = 3 × 0.37
111 = 300 (scaled)
222 = 600
Multiplying by the adjusted Rydberg constant (1.0973933372525…) produces a spiraling sequence:
0.999 = 1.096295943915343…
1.00 = 1.097393337252596…
1.11 = 1.218106604350382…
And so on, potentially revealing patterns if visualized with distinct colors for digits 0–9.
A Fine-Tuning Hypothesis
The numbers 1 to 9 sum to 45, while 1 to 9 (excluding 8) sum to 37. Their ratio, 45 ÷ 37 ≈ 1.216216216…,
echoes the 1.2 factor and hints at fine-tuning possibilities for the Rydberg constant (1.097393690…).
This interplay of numbers—bridging biblical references, atomic physics, and geometric forms—suggests
a deeper, organized structure within the electromagnetic spectrum waiting to be explored.
What do you think—could these adjustments refine our understanding of light and energy?
