Consider two radiations of wavelengths
1. $$\lambda_1 = 2000$$ $$\text{\AA}$$
2. $$\lambda_2 = 6000$$ $$\text{\AA}$$
The ratio of the energies of these two radiations $$\left(\frac{E_1}{E_2}\right)$$ is __________ (Nearest integer).

Step 1: Planck's Equation

The energy $$(E)$$ of a radiation is inversely proportional to its wavelength $$\left(\lambda\right)$$, as given by Planck's equation:

$$E=\frac{hc}{\lambda}$$
Where,

$$h$$ is Planck's constant and

$$c$$ is the speed of light.

Step 2: Determine the ratio

Because $$h$$ and $$c$$ are constants, the ratio of the energies of the two radiations is the inverse ratio of their wavelengths:

$$\frac{E_1}{E_2}=\frac{\lambda_2}{\lambda_1}$$

Step 3: Calculate the Value

$$\frac{E_1}{E_2}=\frac{6000A^{\circ\ }}{2000A^{\circ\ }}=3$$

Therefore, the correct value is 3.