Calculate the following values using velocity of light, c:
a) frequency for 4.50 m light; b) wavenumber for 575 nm light; c) wavelength for 3.1*1018 Hz
radiation; d) wavenumber for 2.5*1011 Hz radiation.
To calculate these values using the velocity of light, c, we can use the following formulas:
a) frequency (f) = c / wavelength (λ)
b) wavenumber (k) = 2π / wavelength (λ)
c) wavelength (λ) = c / frequency (f)
d) wavelength (λ) = 2π / wavenumber (k)
Given:
a) Wavelength (λ) = 4.50 μm = 4.50 × 10^-6 m
b) Wavelength (λ) = 575 nm = 575 × 10^-9 m
c) Frequency (f) = 3.1 × 10^18 Hz
d) Frequency (f) = 2.5 × 10^11 Hz
a) To calculate the frequency for 4.50 μm light:
frequency (f) = c / wavelength (λ)
f = c / λ
f = (3.00 × 10^8 m/s) / (4.50 × 10^-6 m)
f = 6.67 × 10^13 Hz
Therefore, the frequency for 4.50 μm light is 6.67 × 10^13 Hz.
b) To calculate the wavenumber for 575 nm light:
wavenumber (k) = 2π / wavelength (λ)
k = 2π / λ
k = (2π) / (575 × 10^-9 m)
k = 1.09 × 10^7 m^-1
Therefore, the wavenumber for 575 nm light is 1.09 × 10^7 m^-1.
c) To calculate the wavelength for 3.1 × 10^18 Hz radiation:
wavelength (λ) = c / frequency (f)
λ = c / f
λ = (3.00 × 10^8 m/s) / (3.1 × 10^18 Hz)
λ ≈ 9.68 × 10^-11 m
Therefore, the wavelength for 3.1 × 10^18 Hz radiation is approximately 9.68 × 10^-11 m.
d) To calculate the wavenumber for 2.5 × 10^11 Hz radiation:
wavenumber (k) = 2π / wavelength (λ)
k = 2π / λ
k = (2π) / (2.5 × 10^11 Hz)
k ≈ 2.51 × 10^-11 m^-1
Therefore, the wavenumber for 2.5 × 10^11 Hz radiation is approximately 2.51 × 10^-11 m^-1.