calculate the relativistic mass of 1.81x10^24 photons (3.00 mol) with wavelength of 450 nm.

http://en.wikipedia.org/wiki/Mass_in_special_relativity#The_relativistic_energy-momentum_equation

To calculate the relativistic mass of photons, we need to use Einstein's mass-energy equivalence equation, which is E = mc². However, since photons are massless particles, we cannot directly calculate their relativistic mass. Instead, we can calculate the total energy of the given number of photons using the equation E = hc/λ, where E is the energy, h is Planck's constant (6.62607015 × 10⁻³⁴ J⋅s), c is the speed of light (2.998 × 10⁸ m/s), and λ is the wavelength.

Let's calculate the energy of one photon first:

E = hc/λ
= (6.62607015 × 10⁻³⁴ J⋅s × 2.998 × 10⁸ m/s) / (450 × 10⁻⁹ m)
≈ (1.9884 × 10⁻²⁵ J)

Now, we can calculate the total energy of the given number of photons:

Total Energy = E × Number of Photons
= (1.9884 × 10⁻²⁵ J) × (1.81 × 10²⁴ photons)
≈ (3.596604 × 10⁻¹ J)

Since photons do not have rest mass, their relativistic mass is equivalent to their energy. Therefore, the relativistic mass of 1.81 × 10²⁴ photons with a wavelength of 450 nm is approximately 3.596604 × 10⁻¹ J.