Answer to Question #185461 in Physics for Praise

Question

If the ratio of final and intial intensities for 0.1% solution of L-alamine is 5/8( length of beaker is 0.015m.) Determine the ratio of intensities for 0.2% - L-alamine solution in the beaker with length of 0.023m

Answer 1

According to Beer-Lambert law:

$$A=\log\frac{I_0}{I}=klc.$$

For 0.1%-solution and 0.015m-long beaker:

$$\log\frac58=kl_1c_1,\\\space\\ k=\frac{\log(5/8)}{l_1c_1}.$$

For 0.2%-solution and 0.023m-long beaker:

$$\log\frac{I_0}{I}=kl_2c_2,\\\space\\ \log\frac{I_0}{I}=\frac{l_2c_2\log(5/8)}{l_1c_1},\\\space\\ \log\frac{I_0^{c_1l_1}}{I}=\log\frac{5^{l_2c_2}}{8},\\\space\\ I_o^{l_1c_1}=5^{l_2c_2},\\ I_0\approx1.69;\\\space\\ \frac{I_0}{I}\approx\frac{17}{80}.$$