Final answer:
To match each frequency/wavelength pair, we can use the equation c = fλ and calculate the wavelength for each frequency. The correct pairs are: a. λ = 415 nm, b. v = 6.21 x 10¹⁰ Hz, c. λ = 3.12 x 10⁻¹² m.
Step-by-step explanation:
To match each frequency/wavelength pair, we can use the equation c = fλ, where c is the speed of light and is given as 3.00 × 10⁸ m/s. Let's calculate the wavelength for each frequency:
a. For v = 7.23 x 10¹⁴ Hz, we have λ = c / v = (3.00 × 10⁸ m/s) / (7.23 x 10¹⁴ Hz) = 4.14 x 10⁻⁷ m = 415 nm.
b. For v = 6.21 x 10¹⁰ Hz, we have λ = c / v = (3.00 × 10⁸ m/s) / (6.21 x 10¹⁰ Hz) = 4.83 x 10² m = 4.83 mm.
c. For v = 9.62 x 10¹⁹ Hz, we have λ = c / v = (3.00 × 10⁸ m/s) / (9.62 x 10¹⁹ Hz) = 3.12 x 10⁻¹² m.
Hence, the correct pairs are:
a. λ = 415 nm
b. v = 6.21 x 10¹⁰ Hz
c. λ = 3.12 x 10⁻¹² m