Final answer:
The energy carried by a quantum of violet light with a wavelength of 2.59 x 10^-9 m is calculated using the formula E = hc/\u03bb, which gives an energy of 7.682 x 10^-19 joules.
Step-by-step explanation:
The energy carried by a quantum of violet light can be calculated using the equation for the energy of a photon, which is E = hc/\u03bb, where h is Planck's constant (6.626 x 10-34 J·s), c is the speed of light (3.00 x 108 m/s), and \u03bb is the wavelength of the light.
For a violet light with a wavelength of 2.59 x 10-9 m, the energy of a quantum can be calculated as follows:
E = (6.626 x 10-34 J·s) (3.00 x 108 m/s) / (2.59 x 10-9 m)
After calculating, we get:
E = 7.682 x 10-19 J
Therefore, the energy carried by a quantum of violet light with a wavelength of 2.59 x 10-9 m is 7.682 x 10-19 joules.