Question

A sample has Transmittance of 50% when the path length is 10cm. How long would the path length have to be to get a Transmittance of 10%?

Answer 1

Given :

At 50 % transmittance path length is 10 cm

At 10 % transmittance , path length is unknown

Solution :

We use following equation :

% T = exp ( -abc) ….. 1

As we know a absorptivity and c is constant in this problem. Only change in transmittance.

Lets find out path length for 10 % transmittance.

50 = exp ( - 10 cm a x c )

Lets take ln of both side

Ln 50 = - 10 cm ac

3.91 = - 10 cm ac     …..2

For transmittance

Ln 10 = - abc

2.30 = - abc        … 3

Lets take a ratio of equation 2 and 3

3.91 / 2.30 = (- 10 cm ac    )/ - abc        

1.70 b = -10 cm

b = 5.89 cm