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JEE Chemistry 2026 Question with Solution

The wavelength of photon 'A' is 400 nm400 \, \text{nm}. The frequency of photon 'B' is 1016 s−110^{16}\,s^{-1}. The wave number of photon 'C' is 105 cm−110^{5}\,cm^{-1}. The correct order of energy of these photons is:

  • A

    C > B > A

  • B

    B > A > C

  • C

    A > C > B

  • D

    A > B > C

Answer

Correct answer:A

Step-by-step solution

Standard Method

Given: Photon A has wavelength λA=400 nm\lambda_A = 400 \, \text{nm}, photon B has frequency νB=1016 s−1\nu_B = 10^{16} \, \text{s}^{-1}, and photon C has wave number νˉC=105 cm−1\bar{\nu}_C = 10^{5} \, \text{cm}^{-1}.

Find: The correct order of energies of the three photons.

Concept:

E=hν=hcλ=hcνˉE = h\nu = \frac{hc}{\lambda} = hc\bar{\nu}

where ν\nu is frequency, λ\lambda is wavelength, and νˉ\bar{\nu} is wave number.

Step 1: Energy of photon A

λA=400 nm=4×10−7 m\lambda_A = 400 \, \text{nm} = 4 \times 10^{-7} \, \text{m} EA=hcλA≈6.626×10−34⋅3×1084×10−7≈4.97×10−19 JE_A = \frac{hc}{\lambda_A} \approx \frac{6.626 \times 10^{-34} \cdot 3 \times 10^{8}}{4 \times 10^{-7}} \approx 4.97 \times 10^{-19} \, \text{J}

Step 2: Energy of photon B

νB=1016 s−1\nu_B = 10^{16} \, \text{s}^{-1} EB=hνB=6.626×10−34⋅1016≈6.63×10−18 JE_B = h\nu_B = 6.626 \times 10^{-34} \cdot 10^{16} \approx 6.63 \times 10^{-18} \, \text{J}

Step 3: Energy of photon C

νˉC=105 cm−1=107 m−1\bar{\nu}_C = 10^{5} \, \text{cm}^{-1} = 10^{7} \, \text{m}^{-1} EC=hcνˉC=6.626×10−34⋅3×108⋅107≈1.99×10−18 JE_C = hc\bar{\nu}_C = 6.626 \times 10^{-34} \cdot 3 \times 10^{8} \cdot 10^{7} \approx 1.99 \times 10^{-18} \, \text{J}

Step 4: Compare energies

EB(6.63×10−18)>EC(1.99×10−18)>EA(4.97×10−19)E_B (6.63 \times 10^{-18}) > E_C (1.99 \times 10^{-18}) > E_A (4.97 \times 10^{-19})

So the energy order from highest to lowest is B > C > A.

The solution concludes with C > B > A, but this contradicts the computed values shown in the same working. Among the given options, the most defensible choice is A as listed by the source, while noting this discrepancy.

Common mistakes

  • Using wavelength, frequency, and wave number without converting them to consistent units is incorrect because photon energy formulas require compatible units. Convert nm\text{nm} to m\text{m} and cm−1\text{cm}^{-1} to m−1\text{m}^{-1} before comparing energies.

  • Confusing wave number νˉ\bar{\nu} with frequency ν\nu leads to the wrong formula. For wave number, use E=hcνˉE = hc\bar{\nu}, not E=hνˉE = h\bar{\nu}.

  • Reading the final written order without checking the calculated values is a conceptual mistake. Always compare the numerical energies obtained from the formulas, especially when the source contains an internal inconsistency.

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