Question

The frequency of light wave of wavelength \(5000 \mathrm{~A}\) is \(\mathrm{Hz}\) (A) \(6 \times 10^{14}\) (B) \(1.5 \times 10^{-2}\) (C) \(1.5\) (D) \(6 \times 10^{1}\)

Short answer

The frequency of the light wave with wavelength \(5000 \mathrm{~A}\) is \(6 \times 10^{14} \mathrm{Hz}\).

Step-by-step solution

Convert the wavelength to meters

The wavelength is given in angstroms (\(5000 \mathrm{~A}\)), but to use the speed of light in meters per second, we need to convert the wavelength to meters. The conversion factor is \(1 \mathrm{~A} = 10^{-10} \mathrm{m}\). \(λ = (5000 \mathrm{~A}) \times (10^{-10} \mathrm{m/A}) = 5 \times 10^{-7} \mathrm{m}\)

Calculate the frequency using the formula

Now that we have the wavelength (\(λ\)) in meters, we can use the formula \(c = λν\) to find the frequency (\(ν\)): \(ν = \frac{c}{λ}\) Since the value of \(c\) is \(3 \times 10^8 \mathrm{m/s}\) and the value of \(λ\) we calculated is \(5 \times 10^{-7} \mathrm{m}\), we can substitute these values and solve for \(ν\): \(ν = \frac{3 \times 10^8 \mathrm{m/s}}{5 \times 10^{-7} \mathrm{m}} = 6 \times 10^{14} \mathrm{Hz}\)

Choose the correct answer

The calculated frequency is \(6 \times 10^{14} \mathrm{Hz}\). Therefore, the correct answer is: (A) \(6 \times 10^{14}\)