Final answer:
The wavelength of light produced from a mercury lamp with photons having an energy of 4.56 x 10^-19 J is approximately 137.2 nm.
Step-by-step explanation:
To find the wavelength of light produced from a mercury lamp with photons having an energy of 4.56 x 10^-19 J, we can use the equation:
E = hc/λ
Where E is the energy of the photon, h is Planck's constant (6.626 x 10^-34 J s), c is the speed of light (3 x 10^8 m/s), and λ is the wavelength of the light. Rearranging the equation, we get:
λ = hc/E
Plugging in the given values, we have:
λ = (6.626 x 10^-34 J s * 3 x 10^8 m/s) / (4.56 x 10^-19 J)
λ = 1.372 x 10^-7 m or 137.2 nm
Therefore, the wavelength of light produced from the mercury lamp is approximately 137.2 nm.