Question

The quantum yield for the decomposition of HI is 0.2. In an experiment 0.01 moles are decomposed. The number of photons absorbed are:
A.3 \[ \times {10^{22}}\]
B.6 \[ \times {10^{22}}\]
C.8 \[ \times {10^{22}}\]
D.4 \[ \times {10^{22}}\]

Answer 1

Hint:Quantum yield is directly proportional to the number of decayed molecules
Formula used: Quantum Yield = \[\dfrac{{{\text{ }}No.{\text{ }}of{\text{ }}molecules{\text{ }}decomposed}}{{no.{\text{ }}of{\text{ }}photons{\text{ }}absorbed}}\]

 Complete step by step answer:
-According to the hypothesis by the famous Italian Scientist Avogadro, 1 mole of any substance contains \[6.023 \times {10^{23}}\]molecules. The value of \[6.023 \times {10^{23}}\]gm per mole is also known as Avogadro’s number, likely so named after the scientist who has contributed so much to the field of molecular sciences.
- Hence for the given sample of 0.01 moles of HI, the total number of molecules will be equal to:
= 0.01 x \[6.023 \times {10^{23}}\]
= \[6.023 \times {10^{21}}\]
 -Mathematically representing the relation between quantum yield and the number of molecules decompose, we get,
Quantum Yield = \[\dfrac{{{\text{ }}No.{\text{ }}of{\text{ }}molecules{\text{ }}decomposed}}{{no.{\text{ }}of{\text{ }}photons{\text{ }}absorbed}}\]
      \[\therefore \phi = \dfrac{{6.023 \times {{10}^{21}}}}{{No.{\text{ }}of{\text{ }}photons{\text{ }}absorbed}}\]

            No. of photons absorbed = \[\dfrac{{6.023 \times {{10}^{21}}}}{{0.2}}\], since \[\phi \]=0.2 is given
Hence, No. of photons absorbed = \[30.115 \times {10^{21}}\]
                     \[ \approx \] \[3 \times {10^{22}}\]

Hence, Option A is the correct.

Additional information:
 The quantum yield (Φ) of a radiation-induced process is the number of times a specific event occurs per photon absorbed by the system. It can basically be described as a ratio of the number of photons emitted to the number of photons that are absorbed. Quantum yield (Φ) can also be described as a measure of the efficiency of photon emission as defined by the ratio of the number of photons emitted to the number of photons absorbed.

Note:
Quantum yield, defined as the rate at which molecules undergo a given event per photon absorbed per unit time, is well known in photochemistry. Photo Chemists routinely determine quantum yields of reactant disappearance, product formation, light emission, and various other photochemical and photophysical events occurring in photochemical reactions