Question

The value of Planck's constant is 6.63×10⁻³⁴ Joule-second. The velocity of light is 3×10⁸ meters per second. Which value is closest to the wavelength of a quantum of light with a frequency of 8×10¹⁵ Hz?

a. 2.78×10⁻⁷ meters
b. 2.78×10⁻⁸ meters
c. 2.78×10⁻⁹ meters
d. 2.78×10⁻¹⁰ meters

Answer 1

The wavelength of light with a frequency of 8×10^15 Hz is approximately 2.78×10^-8 meters. Option B is correct.

Step-by-step explanation:

The wavelength of light can be calculated using the formula λ = c/f, where λ is the wavelength, c is the speed of light, and f is the frequency. Given that the frequency is 8×10^15 Hz, and the speed of light is 3×10^8 meters per second, we can substitute these values into the formula to find the wavelength: λ = (3×10^8)/(8×10^15) = 3.75×10^-8 meters. Therefore, the closest value to the wavelength of the quantum of light is b. 2.78×10^-8 meters.

The question asks for the wavelength of a quantum of light, given the frequency. Using the formula c = fλ, where c is the speed of light, f is the frequency, and λ is the wavelength, we can rearrange to find λ as λ = c / f. Plugging in the values, we have λ = (3×108 meters per second) / (8×1015 Hz), which gives a wavelength of 3.75×10-8 meters. This value is closest to option b. 2.78×10-8 meters