Final answer:
The wavelength (λ) of light with an energy of 4.22 × 103 J can be calculated using the formula λ = hc/E, and the approximate wavelength calculated is 470 nm, with the closest option being 1.48 × 10-7 m.
Step-by-step explanation:
The question you've asked relates to finding the wavelength of light given its energy in kilojoules. To find the wavelength (λ), we can use the formula E = hc/λ, where E is the energy of the light in joules, h is Planck's constant (6.626 × 10-34 J·s), c is the speed of light (3.00 × 108 m/s), and λ is the wavelength in meters.
As the energy given is in kilojoules, we need to convert it into joules by multiplying it by 103. So the energy in joules is 4.22 × 103 J. Plugging the values into the equation we get:
λ = hc/E
λ = (6.626 × 10-34 J·s × 3.00 × 108 m/s) / (4.22 × 103 J)
After calculating this, you should find that the wavelength of the light is approximately 4.70 × 10-7 meters, which is 470 nm (nanometers), and the closest answer among the options provided is 1.48 × 10-7 m (option b).