which has the longer wavelength, red light of frequency 4.3x10^14 Hz or blue light of frequency 6.4x10^14 Hz. show using calculation by converting your final answer to nanometer

Answer 1

To determine which light has the longer wavelength, we can use the equation:

c = λν

Where:
c = speed of light in a vacuum (3.00 x 10^8 m/s)
λ = wavelength of light
ν = frequency of light

For red light:
ν = 4.3 x 10^14 Hz

For blue light:
ν = 6.4 x 10^14 Hz

Solving for the wavelength of red light:
λ = c / ν
λ = (3.00 x 10^8 m/s) / (4.3 x 10^14 Hz)
λ = 6.98 x 10^-7 m

Solving for the wavelength of blue light:
λ = c / ν
λ = (3.00 x 10^8 m/s) / (6.4 x 10^14 Hz)
λ = 4.69 x 10^-7 m

Therefore, blue light has the longer wavelength compared to red light.

Converting the results to nanometers:
1 m = 1 x 10^9 nm

Wavelength of red light = 6.98 x 10^-7 m x 1 x 10^9 nm/m = 698 nm
Wavelength of blue light = 4.69 x 10^-7 m x 1 x 10^9 nm/m = 469 nm

Therefore, blue light has the longer wavelength of 469 nm compared to red light.