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Structure of Atom question

2022 · 24 Jun · Shift 2 · Q2
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Structure of Atom question

2022 · 24 Jun · Shift 2 · Q2

JEE MainChemistryStructure of AtomMCQ+4 / −1
The energy of one mole of photons of radiation of wavelength 300 nm is (Given : h = 6.63 ×\times× 10 −-− 34 J s, NA = 6.02 ×\times× 1023 mol −-− 1, c = 3 ×\times× 108 m s −-− 1)
  1. A
    235 kJ mol −-− 1
  2. B
    325 kJ mol −-− 1
  3. C
    399 kJ mol −-− 1
  4. D
    435 kJ mol −-− 1
View written solutionFree

Correct answer: C

  1. Energy of one photon

The energy of a photon is given by

E=hcλE = \frac{hc}{\lambda}E=λhc​

Given:

  • h=6.63×10−34 J sh = 6.63 \times 10^{-34}\,\text{J s}h=6.63×10−34J s
  • c=3×108 m s−1c = 3 \times 10^8\,\text{m s}^{-1}c=3×108m s−1
  • λ=300 nm=300×10−9 m=3×10−7 m\lambda = 300\,\text{nm} = 300 \times 10^{-9}\,\text{m} = 3 \times 10^{-7}\,\text{m}λ=300nm=300×10−9m=3×10−7m

So,

E=(6.63×10−34)(3×108)3×10−7E = \frac{(6.63 \times 10^{-34})(3 \times 10^8)}{3 \times 10^{-7}}E=3×10−7(6.63×10−34)(3×108)​

E=6.63×10−19 J per photonE = 6.63 \times 10^{-19}\,\text{J per photon}E=6.63×10−19J per photon

  1. Energy of one mole of photons

Multiply by Avogadro's number:

Emole=(6.63×10−19)(6.02×1023)E_{\text{mole}} = (6.63 \times 10^{-19})(6.02 \times 10^{23})Emole​=(6.63×10−19)(6.02×1023)

Emole=(6.63×6.02)×104 J mol−1E_{\text{mole}} = (6.63 \times 6.02) \times 10^4\,\text{J mol}^{-1}Emole​=(6.63×6.02)×104J mol−1

Emole≈39.9×104 J mol−1E_{\text{mole}} \approx 39.9 \times 10^4\,\text{J mol}^{-1}Emole​≈39.9×104J mol−1

Emole=3.99×105 J mol−1E_{\text{mole}} = 3.99 \times 10^5\,\text{J mol}^{-1}Emole​=3.99×105J mol−1

  1. Convert to kJ mol−1^{-1}−1

3.99×105 J mol−1=399 kJ mol−13.99 \times 10^5\,\text{J mol}^{-1} = 399\,\text{kJ mol}^{-1}3.99×105J mol−1=399kJ mol−1

  1. Match with the options
  • A: 235 kJ mol−1235\,\text{kJ mol}^{-1}235kJ mol−1
  • B: 325 kJ mol−1325\,\text{kJ mol}^{-1}325kJ mol−1
  • C: 399 kJ mol−1399\,\text{kJ mol}^{-1}399kJ mol−1
  • D: 435 kJ mol−1435\,\text{kJ mol}^{-1}435kJ mol−1

Therefore, the correct option is:

C\boxed{\text{C}}C​

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