Question

Frequency of photon having energy \(66 \mathrm{eV}\) is ....... \(\left(\mathrm{h}=6.6 \times 10^{-34} \mathrm{~J} . \mathrm{s}\right)\) (A) \(8 \times 10^{-15} \mathrm{~Hz}\) (B) \(12 \times 10^{-15} \mathrm{~Hz}\) (C) \(16 \times 10^{-15} \mathrm{~Hz}\) (D) \(24 \times 10^{+15} \mathrm{~Hz}\)

Short answer

The frequency of the photon having energy 66 eV is \(16 \times 10^{-15}\mathrm{~Hz}\).

Step-by-step solution

Convert energy to joules

Given energy, E = 66 eV. To convert energy into joules, we can use the conversion factor 1 eV = 1.6 × 10^{-19} J. \(E = 66 \text{ eV} \times \frac{1.6 \times 10^{-19} J}{1 \text{ eV}}\) E = 1.056 × 10^{-17} J Now we have the energy in joules.

Use the formula to find frequency

Now we can use the formula: Energy (E) = Planck's constant (h) × Frequency (ν) We are given Planck's constant, h = 6.6 × 10^{-34} J·s. We can rearrange the formula to find the frequency: \(ν = \frac{E}{h}\) Plug in the values for E and h: \(ν = \frac{1.056 \times 10^{-17} J}{6.6 \times 10^{-34} J.s}\)

Calculate the frequency and select the correct option

After dividing the energy by Planck's constant, we get the frequency: ν = 1.6 × 10^{16} Hz We can write this in scientific notation as: ν = 16 × 10^{15} Hz Comparing this value to the available options, we see that it matches option (C): (C) \(16 \times 10^{-15} \mathrm{~Hz}\) So the frequency of the photon having energy 66 eV is \(16 \times 10^{-15}\mathrm{~Hz}\). Option (C) is the correct answer.