Question:
A protein solution of 1 µM has transmission of 40 % at 280 nm, when measured in a 1 cm cuvette using a UV-Visible spectrophotometer. The transmission of the same solution, when measured using a 2 cm cuvette is ______ %. (rounded off to the nearest integer)
A protein solution of 1 µM has transmission of 40 % at 280 nm, when measured in a 1 cm cuvette using a UV-Visible spectrophotometer. The transmission of the same solution, when measured using a 2 cm cuvette is ______ %. (rounded off to the nearest integer)
Updated On: Nov 18, 2025
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Correct Answer: 16
Solution and Explanation
To solve this problem, we use the Beer-Lambert Law which relates absorbance (A) to concentration (c), path length (l), and molar absorptivity (ε) as A = εcl. Transmission (T) is related to absorbance by the equation A = -log(T). Transmission is given as a percentage, so T = 40% = 0.40 when the cuvette is 1 cm.
First, calculate absorbance for the 1 cm cuvette:
A1 = -log(0.40).
Then, for a 2 cm cuvette, the path length doubles, hence:
A2 = ε(2c)
Since the absorbance is proportional to the path length and concentration is constant, A2 = 2A1.
Calculate A2 = 2 × -log(0.40).
Convert A2 back to transmission for the 2 cm cuvette:
T2 = 10-A2,
where T2 is the transmission in decimal form.
Finally, convert T2 back to a percentage: T2 % = T2 × 100.
Performing these calculations, A1 = -log(0.40) ≈ 0.398. Therefore, A2 = 2 × 0.398 ≈ 0.796.
Now, calculate T2:
T2 = 10-0.796 ≈ 0.159
T2 % = 0.159 × 100 ≈ 16%.
Thus, the transmission of the solution in a 2 cm cuvette is 16%. This value is within the range [16, 16].
First, calculate absorbance for the 1 cm cuvette:
A1 = -log(0.40).
Then, for a 2 cm cuvette, the path length doubles, hence:
A2 = ε(2c)
Since the absorbance is proportional to the path length and concentration is constant, A2 = 2A1.
Calculate A2 = 2 × -log(0.40).
Convert A2 back to transmission for the 2 cm cuvette:
T2 = 10-A2,
where T2 is the transmission in decimal form.
Finally, convert T2 back to a percentage: T2 % = T2 × 100.
Performing these calculations, A1 = -log(0.40) ≈ 0.398. Therefore, A2 = 2 × 0.398 ≈ 0.796.
Now, calculate T2:
T2 = 10-0.796 ≈ 0.159
T2 % = 0.159 × 100 ≈ 16%.
Thus, the transmission of the solution in a 2 cm cuvette is 16%. This value is within the range [16, 16].
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