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)

Answer 1

Correct Answer: 16

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].