26. Which of the following statements is/are CORRECT?
(A) Absorption occurs at all wavelengths if light passes through a given solution.
(B) The efficiency of a photochemical process is often expressed in terms of quantum yield.
(C) The unit of molar extinction coefficient is litre mole-1cm.
(D) The extent of absorption in a dilute solution would be the same if the concentration is doubled and the path-length of light passing through solution is halved.
Which Statements About Light Absorption, Quantum Yield, and Molar Extinction Coefficient Are Correct?
Understanding the Basic Principles Behind the Question
This question combines four important concepts of spectroscopy and photochemistry: selective absorption of electromagnetic radiation, quantum yield, the unit of molar extinction coefficient, and the Beer-Lambert law. To identify the correct statements, each option must be examined independently.
The central equation required for understanding the absorption-related statements is the Beer-Lambert law:
A = εcl
where A is the absorbance, ε is the molar extinction coefficient or molar absorptivity, c is the concentration of the absorbing species, and l is the path length through which light travels in the solution.
According to this equation, absorbance depends directly on both concentration and path length. The product cl is particularly important in determining whether a change in concentration can be compensated for by an opposite change in path length.
Detailed Explanation of Statement (A)
Statement (A): Absorption occurs at all wavelengths if light passes through a given solution.
Statement (A) is incorrect.
A chemical substance does not normally absorb electromagnetic radiation equally at all wavelengths. Instead, absorption is a selective process. A molecule absorbs radiation only when the energy of the incident photon matches the energy difference between two allowed molecular energy states.
The energy of electromagnetic radiation is expressed as:
E = hν = hc/λ
where E is the energy of the photon, h is Planck’s constant, ν is the frequency, c is the speed of light, and λ is the wavelength.
Because molecules possess specific quantized energy levels, only photons with appropriate energies can produce transitions between these levels. Therefore, a given compound absorbs strongly at certain wavelengths and weakly or not at all at other wavelengths.
Why Absorption Is Wavelength-Specific
When light containing a range of wavelengths passes through a solution, only particular wavelengths may be absorbed by the molecules present in that solution. The remaining wavelengths are transmitted.
For example, in UV-visible spectroscopy, molecules absorb ultraviolet or visible radiation when the photon energy is sufficient to promote electrons from lower-energy molecular orbitals to higher-energy molecular orbitals. Common electronic transitions include π → π* and n → π* transitions.
Since the energy difference between molecular orbitals is specific for a particular molecule, the wavelength required to cause an electronic transition is also specific. This is why absorption spectra contain characteristic absorption bands rather than continuous absorption at every wavelength.
Therefore, the statement that absorption occurs at all wavelengths is scientifically incorrect.
Conclusion for Statement (A): Incorrect
Detailed Explanation of Statement (B)
Statement (B): The efficiency of a photochemical process is often expressed in terms of quantum yield.
Statement (B) is correct.
Quantum yield is one of the most important parameters used to express the efficiency of a photochemical process. It describes how effectively absorbed photons produce a particular photochemical event.
The quantum yield, represented by the symbol Φ, is generally defined as:
Φ = Number of molecules undergoing the specified photochemical event / Number of photons absorbed
In terms of moles, it may also be expressed as:
Φ = Moles of molecules transformed / Moles of photons absorbed
A photon is also referred to as a quantum of electromagnetic radiation. Therefore, quantum yield directly relates the number of photochemical events to the number of photons absorbed by the system.
Why Quantum Yield Measures Photochemical Efficiency
Suppose a sample absorbs 100 photons and 100 molecules undergo the desired photochemical transformation. The quantum yield would be:
Φ = 100/100 = 1
A quantum yield of 1 indicates that, on average, one photochemical event occurs for every photon absorbed.
If only 50 molecules react after the absorption of 100 photons, then:
Φ = 50/100 = 0.5
This means that only half of the absorbed photons effectively produce the specified photochemical event.
Thus, quantum yield provides a direct and meaningful measure of the efficiency of a photochemical process.
Can Quantum Yield Be Greater Than One?
In some photochemical reactions, the quantum yield can be greater than one. This may occur in chain reactions where the absorption of a single photon initiates a sequence of chemical reactions involving several molecules.
Therefore, quantum yield is not always restricted to values between zero and one. Its numerical value depends on the mechanism of the photochemical process being studied.
Since quantum yield is widely used to express photochemical efficiency, Statement (B) is correct.
Conclusion for Statement (B): Correct
Detailed Explanation of Statement (C)
Statement (C): The unit of molar extinction coefficient is litre mole⁻¹ cm.
Statement (C) is incorrect as written.
The correct unit of the molar extinction coefficient is:
L mol⁻¹ cm⁻¹
The important point is that the centimetre term must have the exponent −1, not +1.
To understand why, consider the Beer-Lambert law:
A = εcl
Rearranging the equation gives:
ε = A/cl
Absorbance A is dimensionless. Concentration c is commonly expressed in:
mol L⁻¹
Path length l is commonly expressed in:
cm
Therefore:
ε = 1 / [(mol L⁻¹)(cm)]
Simplifying the units:
ε = L mol⁻¹ cm⁻¹
Thus, the standard unit of molar extinction coefficient or molar absorptivity is:
litre mole⁻¹ centimetre⁻¹
or
L mol⁻¹ cm⁻¹
What Is the Molar Extinction Coefficient?
The molar extinction coefficient is a measure of how strongly a chemical species absorbs light at a particular wavelength. A substance with a high molar extinction coefficient absorbs light strongly, whereas a substance with a low molar extinction coefficient absorbs less strongly under the same concentration and path-length conditions.
The value of the molar extinction coefficient depends on the absorbing molecule and the wavelength at which the measurement is made. Therefore, it is commonly reported together with a specified wavelength.
Because Statement (C) gives the unit as litre mole⁻¹ cm rather than litre mole⁻¹ cm⁻¹, the statement is incorrect.
Conclusion for Statement (C): Incorrect
Detailed Explanation of Statement (D)
Statement (D): The extent of absorption in a dilute solution would be the same if the concentration is doubled and the path-length of light passing through solution is halved.
Statement (D) is correct.
This statement follows directly from the Beer-Lambert law:
A = εcl
For a particular substance at a fixed wavelength, the molar extinction coefficient ε remains constant. Therefore, absorbance depends on the product of concentration and path length:
A ∝ cl
Suppose the initial concentration is c and the initial path length is l. The initial absorbance is:
A₁ = εcl
Now, the concentration is doubled:
New concentration = 2c
At the same time, the path length is halved:
New path length = l/2
The new absorbance becomes:
A₂ = ε(2c)(l/2)
Simplifying:
A₂ = εcl
Therefore:
A₂ = A₁
The absorbance remains unchanged.
Why Doubling Concentration and Halving Path Length Cancel Each Other
Increasing the concentration means that a greater number of absorbing molecules are present per unit volume. This tends to increase the amount of light absorbed.
In contrast, reducing the path length means that light travels through a shorter distance within the absorbing solution. This tends to decrease the amount of light absorbed.
When the concentration is doubled and the path length is simultaneously halved, these two effects exactly compensate for each other because the product cl remains constant.
Initially:
cl
After the changes:
(2c)(l/2) = cl
Since the product of concentration and path length remains unchanged, the absorbance also remains unchanged.
Therefore, Statement (D) is correct.
Conclusion for Statement (D): Correct
Understanding the Beer-Lambert Law in Detail
The Beer-Lambert law establishes a quantitative relationship between the absorption of light and the properties of the absorbing solution. The equation is:
A = εcl
The absorbance can also be related to incident and transmitted light intensities by:
A = log₁₀(I₀/I)
where I₀ is the intensity of incident light and I is the intensity of transmitted light.
This relationship means that as the concentration of an absorbing substance increases, less light is transmitted through the solution and absorbance increases. Similarly, increasing the path length allows the light to interact with more absorbing molecules, which also increases absorbance.
For dilute solutions under suitable experimental conditions, absorbance is directly proportional to both concentration and path length.
Relationship Between Absorbance, Concentration, and Path Length
The proportional relationship can be written as:
A ∝ c
when the path length and molar extinction coefficient remain constant.
Similarly:
A ∝ l
when concentration and molar extinction coefficient remain constant.
Combining both relationships gives:
A ∝ cl
This explains why doubling the concentration alone would double the absorbance and why halving the path length alone would reduce the absorbance by half.
However, when both changes occur simultaneously:
2 × 1/2 = 1
Therefore, there is no net change in absorbance.
This mathematical relationship is the reason Statement (D) is correct.
Difference Between Absorption and Transmission
When light passes through a solution, some wavelengths may be absorbed while others may be transmitted. The fraction of incident light that passes through the sample is called transmittance.
Transmittance is expressed as:
T = I/I₀
where I is the transmitted light intensity and I₀ is the incident light intensity.
Absorbance is related to transmittance by:
A = −log₁₀T
Therefore, greater absorption corresponds to lower transmittance, while lower absorption corresponds to higher transmittance.
This relationship also helps explain why molecules do not absorb equally at all wavelengths. At wavelengths where the molecule absorbs strongly, transmittance decreases. At wavelengths where the molecule does not absorb significantly, most of the light passes through the sample.
Importance of Quantum Yield in Photochemistry
Quantum yield is especially useful in photochemistry because the absorption of light is only the first step of a photochemical process. After absorbing a photon, a molecule may undergo several possible processes.
It may participate in a chemical reaction, release energy as fluorescence, release energy as phosphorescence, undergo non-radiative relaxation, or transfer energy to another molecule.
Therefore, not every absorbed photon necessarily produces the desired photochemical reaction. Quantum yield allows scientists to determine how efficiently absorbed light is converted into a specific chemical or physical event.
A high quantum yield indicates an efficient process, whereas a low quantum yield indicates that many absorbed photons are lost through competing pathways.
Evaluation of All Four Statements
Statement (A) is incorrect because absorption does not occur at all wavelengths. Molecules selectively absorb radiation at wavelengths corresponding to allowed energy transitions.
Statement (B) is correct because the efficiency of a photochemical process is commonly expressed in terms of quantum yield.
Statement (C) is incorrect because the correct unit of the molar extinction coefficient is L mol⁻¹ cm⁻¹, not L mol⁻¹ cm.
Statement (D) is correct because, according to the Beer-Lambert law, absorbance depends on the product cl. Doubling concentration and halving path length leave this product unchanged.
Final Answer
The correct statements are:
(B) The efficiency of a photochemical process is often expressed in terms of quantum yield.
and
(D) The extent of absorption in a dilute solution would be the same if the concentration is doubled and the path length is halved.
Therefore:
Correct Answer: (B) and (D)
