Consider two radiations of wavelengths 1. λ1 = 2000 Å 2. λ2 = 6000 Å The ratio of the energies of these two radiations (E1/E2) is _______ (Nearest integer).

The correct answer is Option 3. Full mathematical solution steps and hints are accessible in the interactive StemCET workspace.

Chemistry Q73 – JEE-MAIN 2026

Consider two radiations of wavelengths 1.

λ_{1} = 2000 Å

λ_{2} = 6000 Å

The ratio of the energies of these two radiations

(\frac{E_{1}}{E_{2}})

is _______ (Nearest integer).

Enter Calculated Numerical Value:

The energy of electromagnetic radiation is inversely proportional to its wavelength.

Step 1: Recall the relationship between energy and wavelength✦ Active

The energy of a photon is inversely proportional to its wavelength. This relationship is given by Planck's equation:

E = \frac{h c}{λ}

where $h$ is Planck's constant, $c$ is the speed of light, and $λ$ is the wavelength.

Step 2: Set up the ratio of energies○ Expand

For two radiations with energies $E_{1}$ and $E_{2}$ and wavelengths $λ_{1}$ and $λ_{2}$ respectively, the ratio is:

\frac{E_{1}}{E_{2}} = \frac{\frac{h c}{λ_{1}}}{\frac{h c}{λ_{2}}} = \frac{λ_{2}}{λ_{1}}

💡 Teacher's Secret Hint

Notice that $h c$ cancels out, simplifying the calculation significantly.

Step 3: Substitute the given values and calculate○ Expand

Given $λ_{1} = 2000 Å$ and $λ_{2} = 6000 Å$ . Substitute these values into the ratio expression:

\frac{E_{1}}{E_{2}} = \frac{6000 Å}{2000 Å} = 3

The ratio of the energies is 3. The nearest integer is 3.

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