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# 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 $\times {10^{22}}$

Last updated date: 12th Sep 2024
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Hint:Quantum yield is directly proportional to the number of decayed molecules
Formula used: Quantum Yield = $\dfrac{{{\text{ }}No.{\text{ }}of{\text{ }}molecules{\text{ }}decomposed}}{{no.{\text{ }}of{\text{ }}photons{\text{ }}absorbed}}$

-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.