a. What is the frequency of radiation that has a wavelength of 11 μm, about the size of a bacterium? b. What is the wavelength of radiation that has a frequency of 5.30*10^14 s^-1? c. Would the radiations in part (a) or part (b) be visible to the human eye? d. What distance does electromagnetic radiation travel in 45.0 μs?

a) ν = 2.7 x 10¹³ s⁻¹

b) λ = 5.7 x 10⁻⁷ m

c) Neither will be visible

d) d = 13,500 m

Explanation:

The relationship ν = c/λ where

ν = frequency of the radiation

c = speed of light = 3 x 10^8 m/s

λ = wavelength of the radiation

will be used to solve parts a), b) and c).

For part d. we know that all electromagnetic radiation travel at the speed of light so d = speed x time

a) ν = 3 x 10^8 m/s / 11 x 10 ⁻⁶ m (1 μm = 10⁻6 m)

= 2.7 x 10¹³ s⁻¹

b) λ = c/ν = 3 x 10^8 m/s / 5.30 x 10¹⁴ s⁻¹ = 5.7 x 10⁻⁷ m

c) The visible spectrum range is 380 to 470 nm

in a. converting to nm:

11 x 10⁻⁶ m x 10⁹ nm/m = 11,000 nm

in b. converting to nm:

5.7 x 10⁻⁷ m x 10⁹ nm / m = 570 nm

Neither of these radiations will be visible to the human eye.

d) d = 3 x 10^8 m/s x 45 x 10⁻⁶ s = 13,500 m