5. As mentioned in the text, the fraction F of light that is absorbed by any gas

Question

5. As mentioned in the text, the fraction F of light that is absorbed by any gas in air is logarith- mically related to the concentration C of the gas and the distance d through which the light travels; this relationship is called the Beer-Lambert law: ng le loge(1-F) = _KCd Here K is a proportionality constant. Show by simple trial calculations that for concentrations near zero (eg, where KCd = 0.001), F is related almost linearly to C, whereas for larger KCd values (e.g., near 2), doubling the concentration does not nearly double the light absorption.

Explanation / Answer

log (1-F) when expanded in taylor series

log (1-F)= -F + F2/2-F3/3 + . + .                   =-KCd

when KCd is =0.001

log (1-F)=-0.001

1-F= 0.999

F= 1-0.999=0.001

F is small and for small values, higher terms of taylor series can be neglected.

Hence -F =-KCd, or F is proportional to C.

2. When KCd= 2

log (1-F)= -2

1-F= 0.135

F= 1-0.135=0.865

since F is large, higher terms cannot be nelgected. Hence

hence when concentration is doubled, KCd=4

log (1-f)=-4

F=0.98

Hence fraction of light absorbed is not doubled.

Related Questions

Navigate

• Browse (All)
• Browse 5
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.