A Transmittance to Absorbance Calculator is used in spectroscopy to convert between two related measurements of light interaction with a sample: transmittance and absorbance.
For example, if a solution allows 50% of light to pass through (transmittance of 0.5 or 50%), the calculator would determine its absorbance as approximately 0.301.
This conversion is particularly useful in fields like biochemistry, where absorbance measurements are often used to determine the concentration of substances in solution.
Transmittance to Absorbance Calculator
| Transmittance (%) | Transmittance (decimal) | Conversion Equation | Absorbance |
|---|---|---|---|
| 100 | 1.000 | A = -log₁₀(1.000) | 0.000 |
| 50 | 0.500 | A = -log₁₀(0.500) | 0.301 |
| 25 | 0.250 | A = -log₁₀(0.250) | 0.602 |
| 10 | 0.100 | A = -log₁₀(0.100) | 1.000 |
| 5 | 0.050 | A = -log₁₀(0.050) | 1.301 |
| 1 | 0.010 | A = -log₁₀(0.010) | 2.000 |
| 0.1 | 0.001 | A = -log₁₀(0.001) | 3.000 |
Transmittance to Absorbance Formula
The formula used to convert transmittance to absorbance is:
A = -log₁₀(T)
Where:
- A is absorbance (unitless)
- T is transmittance (expressed as a decimal between 0 and 1)
For transmittance expressed as a percentage, the formula becomes:
A = -log₁₀(%T / 100)
This logarithmic relationship means that as transmittance decreases, absorbance increases, but not in a linear fashion. For instance:
- A transmittance of 100% (T = 1) yields an absorbance of 0
- A transmittance of 10% (T = 0.1) results in an absorbance of 1
- A transmittance of 1% (T = 0.01) gives an absorbance of 2
What is the absorbance of 20% transmittance?
To calculate the absorbance of a sample with 20% transmittance, we apply the formula:
A = -log₁₀(20 / 100) = -log₁₀(0.2)
Using a calculator or logarithm tables, we find that log₁₀(0.2) ≈ -0.69897.
Therefore, A = -(-0.69897) ≈ 0.69897.
This result demonstrates that a sample allowing only 20% of light to pass through (i.e., absorbing 80% of the incident light) has an absorbance of approximately 0.699.
How to determine transmittance (% T) from Beer Lambert’s law?
Beer-Lambert’s law relates the attenuation of light to the properties of the material through which it is traveling.
The Beer-Lambert law is expressed as:
A = εbc
Where:
- A is absorbance
- ε is the molar attenuation coefficient (L mol⁻¹ cm⁻¹)
- b is the path length of the sample (cm)
- c is the concentration of the absorbing species (mol L⁻¹)
To determine transmittance from Beer-Lambert’s law, we can use the relationship between absorbance and transmittance:
T = 10⁻ᴬ
Substituting the Beer-Lambert equation:
T = 10⁻ᵋᵇᶜ
To express this as a percentage:
%T = 100 × 10⁻ᵋᵇᶜ
This formula allows us to calculate transmittance if we know the molar attenuation coefficient, path length, and concentration of the sample.
For example, if ε = 1000 L mol⁻¹ cm⁻¹, b = 1 cm, and c = 0.001 mol L⁻¹, we can calculate:
%T = 100 × 10⁻¹⁰⁰⁰×¹×⁰·⁰⁰¹ ≈ 10%
What is the relationship between transmittance and absorbance?
Transmittance and absorbance are inversely related, with absorbance being a logarithmic function of transmittance.
Their relationship can be expressed in several equivalent ways:
- A = -log₁₀(T)
- T = 10⁻ᴬ
- A = log₁₀(1/T)
- T = 1/10ᴬ
This relationship means that:
- As transmittance decreases, absorbance increases (and vice versa)
- The relationship is not linear; small changes in transmittance at low values correspond to large changes in absorbance
- Absorbance can theoretically range from 0 to infinity, while transmittance is bounded between 0 and 1 (or 0% to 100%)
- A transmittance of 100% corresponds to an absorbance of 0
- A transmittance of 10% corresponds to an absorbance of 1
- A transmittance of 1% corresponds to an absorbance of 2
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