Step 1: Principle of photoelectric effect.
The stopping potential depends only on the energy of the photons (i.e., frequency of light), not on intensity or power.
Step 2: Effect of doubling the light power.
Doubling the power doubles the number of photons hitting the metal surface, thus increasing the number of emitted electrons. However, since photon energy remains constant, the stopping potential does not change.
Step 3: Conclusion.
Hence, when the power of the light source is doubled, the stopping potential remains the same.

At a particular temperature T, Planck's energy density of black body radiation in terms of frequency is \(\rho_T(\nu) = 8 \times 10^{-18} \text{ J/m}^3 \text{ Hz}^{-1}\) at \(\nu = 3 \times 10^{14}\) Hz. Then Planck's energy density \(\rho_T(\lambda)\) at the corresponding wavelength (\(\lambda\)) has the value \rule{1cm}{0.15mm} \(\times 10^2 \text{ J/m}^4\). (in integer)
[Speed of light \(c = 3 \times 10^8\) m/s]
(Note: The unit for \(\rho_T(\nu)\) in the original problem was given as J/m³, which is dimensionally incorrect for a spectral density. The correct unit J/(m³·Hz) or J·s/m³ is used here for the solution.)