Question

If 1 M of a dye in water transmits 50% of incident light at 400 nm, then 2 M of the dye in water transmits _______ % of the incident light at 400 nm. (rounded off to the nearest integer)
[Given: Both experiments are performed in the same spectrophotometric cell.]

Answer 1

Correct Answer: 25

The transmission of light through a solution follows the Beer-Lambert Law, which is given by:

T = \( 10^{-\epsilon cl} \)

Where:

• T is the transmission
• \( \epsilon \) is the molar absorptivity
• c is the concentration of the solution
• l is the path length of the cell

Since the experiments are performed in the same spectrophotometric cell, the path length \( l \) is constant for both cases. We are given that:

• 1 M of dye transmits 50% of the incident light.

Now, when the concentration is doubled to 2 M, the transmission of light decreases according to the Beer-Lambert Law because absorbance increases with concentration. For a 2 M solution, the transmission would be halved:

Transmission at 2 M = \( \frac{50}{2} = 25\% \)

Thus, the 2 M dye transmits 25% of the incident light.