Final answer:
To find the energy of a violet photon with a wavelength of 413 nm (assuming a typo in the provided value), convert the wavelength to meters and use the formula E = (h*c)/λ with Planck's constant and the speed of light in standard units. The calculated energy is approximately 4.81 x 10^-19 J.
Step-by-step explanation:
To calculate the energy of a photon of light with a given wavelength, one can use the following equation that relates energy (E), Plancks constant (h), light speed (c), and wavelength (λ): E = (h*c)/λ. To use this equation, the values of Planck's constant h (6.626 x 10-34 J·s) and the speed of light c (approximately 3.00 x 108 m/s) should be in their standard units. Also, the wavelength should be converted from nanometers to meters. In this question, the violet light has a wavelength of 4.13 x 107 nm, but the value seems to be incorrectly provided as it exceeds the typical range for visible light (400-700 nm). Assuming a typo and the actual value might be 413 nm (4.13 x 10-7 m), we can apply the equation.
First, convert the wavelength from nanometers to meters by moving the decimal nine places to the left (1 nm = 1 x 10-9 m), giving us 4.13 x 10-7 m. Then apply the equation:
E = (6.626 x 10-34 J·s * 3.00 x 108 m/s) / (4.13 x 10-7 m)
E = (1.988 x 10-25 J·m) / (4.13 x 10-7 m)
E ≈ 4.81 x 10-19 J
The energy of a single photon of this violet light is approximately 4.81 x 10-19 joules.