QInteger TypeAtomic Structure
Consider two radiations of wavelengths: (1) $\lambda_1 = 2000$ Å and (2) $\lambda_2 = 6000$ Å.
The ratio of the energies of these two radiations $E_1/E_2$ is __________ (Nearest integer).
✅ Correct Answer
3
Solution
1
Use Planck-Einstein relation

Energy of a photon: $E = h\nu = \dfrac{hc}{\lambda}$

Energy is inversely proportional to wavelength: $E \propto \dfrac{1}{\lambda}$

2
Calculate the ratio
$$\frac{E_1}{E_2} = \frac{hc/\lambda_1}{hc/\lambda_2} = \frac{\lambda_2}{\lambda_1} = \frac{6000}{2000} = \boxed{3}$$

The radiation with shorter wavelength (2000 Å) has 3 times more energy than the radiation with longer wavelength (6000 Å).

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Theory & Key Concepts
Planck's Quantum Theory and Photon Energy

Planck's equation: $E = h\nu = \dfrac{hc}{\lambda}$, where $h = 6.626\times10^{-34}$ J·s (Planck's constant), $c = 3\times10^8$ m/s (speed of light), $\nu$ = frequency (Hz), $\lambda$ = wavelength (m).

Key relationship: Since $c = \nu\lambda$, we have $\nu = c/\lambda$. Substituting: $E = hc/\lambda$. So energy is inversely proportional to wavelength — shorter wavelength means higher energy photon.

Electromagnetic spectrum in order of increasing energy: Radio < Microwave < Infrared < Visible < UV < X-ray < Gamma rays. Correspondingly, wavelength decreases in this order.

Visible light wavelengths: 400 nm (violet) to 700 nm (red). The two wavelengths here: 2000 Å = 200 nm (UV region) and 6000 Å = 600 nm (orange-red visible). UV photons are 3× more energetic.

Angstrom to nm: 1 Å = 10⁻¹⁰ m = 0.1 nm. So 2000 Å = 200 nm and 6000 Å = 600 nm. Always confirm units before comparing.

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Important Concepts
E = hc/λ Formula

Energy of a photon E=hc/λ. Here h and c are constants. For ratio E₁/E₂=λ₂/λ₁=6000/2000=3. Short wavelength radiation is more energetic.

Why UV is More Energetic Than Visible

2000 Å = 200 nm falls in the UV range. 6000 Å = 600 nm is orange-red visible light. UV photons have energy ~6.2 eV while orange photons have ~2.1 eV — ratio ≈3. UV can break chemical bonds; visible light generally cannot.

Inverse Proportionality

E∝1/λ. If λ doubles, E halves. If λ is 3× larger, E is 3× smaller. Here λ₂=3λ₁, so E₁=3E₂.

Converting Angstroms to Metres

1 Å = 10⁻¹⁰ m. 2000 Å = 2×10⁻⁷ m. 6000 Å = 6×10⁻⁷ m. For ratio calculation, units cancel as long as both are in the same unit.

FAQs
1
What is E₁/E₂?
E₁/E₂ = λ₂/λ₁ = 6000/2000 = 3.
2
Why does E∝1/λ?
E=hc/λ. Since h and c are constants, E is inversely proportional to λ.
3
What region of EM spectrum is 2000 Å?
2000 Å = 200 nm, which is in the UV (ultraviolet) region. 6000 Å = 600 nm is orange visible light.
4
What is the actual energy of a 2000 Å photon?
E=hc/λ=6.63×10⁻³⁴×3×10⁸/(2×10⁻⁷)=9.9×10⁻¹⁹ J ≈ 6.2 eV.
5
Is this from JEE Main 2026?
Yes, this appeared in JEE Main 2026 Chemistry Section B.
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