Question

Most retinal tears and detachments are treated by photocoagulation with a laser. A commonly used laser is one with a wavelength of \(514 \mathrm{nm} .\) Calculate (a) the frequency. (b) the energy in joules/photon. (c) the energy in \(\mathrm{kJ} / \mathrm{mol}\).

Short answer

Answer: The frequency of the laser is \(5.84 \times 10^{14} \, \mathrm{Hz}\), the energy per photon is \(3.87 \times 10^{-19} \, \mathrm{J}\), and the energy in kJ/mol is \(233 \, \mathrm{kJ/mol}\).

Step-by-step solution

Find the frequency

First, let's find the frequency of the laser using the formula mentioned above: $$v = \frac{c}{\lambda}$$ Given the wavelength (\(\lambda= 514 \, \mathrm{nm}\)), we convert it to meters: $$\lambda = 514 \times 10^{-9} \, \mathrm{m}$$ Now, we can calculate the frequency: $$v = \frac{3.0 \times 10^8 \, \mathrm{m/s}}{514 \times 10^{-9} \, \mathrm{m}}$$

Calculate the frequency

Now let's calculate the frequency, v: $$v = \frac{3.0 \times 10^8 \, \mathrm{m/s}}{514 \times 10^{-9} \, \mathrm{m}} \approx 5.84 \times 10^{14} \, \mathrm{Hz}$$ The frequency of the laser is \(5.84 \times 10^{14} \, \mathrm{Hz}\).

Find the energy per photon

Using the calculated frequency and Planck's constant, we can find the energy per photon: $$E = h \cdot v$$

Calculate the energy per photon

Let's calculate the energy per photon, E: $$E = (6.63\times 10^{-34} \,\mathrm{J\cdot s}) \cdot (5.84\times 10^{14} \,\mathrm{Hz}) \approx 3.87 \times 10^{-19} \, \mathrm{J}$$ The energy per photon is \(3.87 \times 10^{-19} \, \mathrm{J}\).

Find the energy in kJ/mol

To find the energy in kJ/mol, we will multiply the energy per photon by Avogadro's number, and then convert Joules to kJ: $$E_{\mathrm{kJ/mol}} = E_{\mathrm{J/photon}} \cdot N_{\mathrm{A}} \cdot \frac{1 \mathrm{kJ}}{1000 \mathrm{J}}$$

Calculate the energy in kJ/mol

Let's calculate the energy in kJ/mol: $$E_{\mathrm{kJ/mol}} = (3.87 \times 10^{-19} \, \mathrm{J}) \cdot (6.022 \times 10^{23} \, \mathrm{mol^{-1}}) \cdot \frac{1 \mathrm{kJ}}{1000 \mathrm{J}} \approx 233 \, \mathrm{kJ/mol}$$ The energy in kJ/mol is \(233 \, \mathrm{kJ/mol}\). To summarize: (a) The frequency of the laser is \(5.84 \times 10^{14} \, \mathrm{Hz}\). (b) The energy per photon is \(3.87 \times 10^{-19} \, \mathrm{J}\). (c) The energy in kJ/mol is \(233 \, \mathrm{kJ/mol}\).