Use the equations above to answer the following questions 1. Ultraviolet radiation has a frequency of 6.8times 10^15Hz Calculate the energy, in joules, of the photon. 2. Find the energy in joules per photon,of microwave radiation with a frequency of 7.91times 10^10Hz 3. A sodium vapor lamp emits light photons with a wavelength of 5.89times 10^-7m . What is the energy of th photons? 4. One of the electron transitions in a hydrogen atom produces infrared light with a wavelength of 746. What amount of energy causes this transition? 5. Find the energy in kJ for an x-ray photon with a frequency of 2.4times 10^18s^-1 6. A ruby laser produces red light that has a wavelength of 500 nm. Calculate its energy in joules. 7. What is the frequency of UV light that has an energy of 2.39times 10^-18J 8. What is the wavelength and frequency of photons with an energy of 1.4times 10^-21J 9. What is the energy of a light that has 434 nm? 10. What is the wavelength of a light that has a frequency of 3.42times 10^11Hz

1. The energy of a photon can be calculated using the equation:<br />$E = hf$<br />where $E$ is the energy, $h$ is Planck's constant ($6.626 \times 10^{-34} \, \text{J} \cdot \text{s}$), and $f$ is the frequency.<br /><br />Given that the frequency of ultraviolet radiation is $6.8 \times 10^{15} \, \text{Hz}$, we can substitute the values into the equation:<br />$E = (6.626 \times 10^{-34} \textcdot \text{s}) \times (6.8 \times 10^{15} \, \text{Hz})$<br /><br />Calculating this gives us:<br />$E = 4.51 \times 10^{-18} \, \text{J}$<br /><br />Therefore, the energy of the photon is $4.51 \times 10^{-18} \, \text{J}$.<br /><br />2. Using the same equation as in question 1, we can calculate the energy of microwave radiation with a frequency of $7.91 \times 10^{10} \, \text{Hz}$:<br />$E = (6.626 \times 10^{-34} \, \text{J} \cdot \text{s}) \times (7.91 \10} \, \text{Hz})$<br /><br />Calculating this gives us:<br />$E = 5.24 \times 10^{-23} \, \text{J}$<br /><br />Therefore, the energy of the photon is $5.24 \times 10^{-23} \, \text{J}$.<br /><br />3. The energy of a photon can also be calculated using the equation:<br />$E = \frac{hc}{\lambda}$<br />where $E$ is the energy, $h$ is Planck's constant, $c$ is the speed of light ($3.00 \times 10^8 \, \text{m/s}$), and $\lambda$ is the wavelength.<br /><br />Given that the wavelength of the sodium vapor lamp is $5.89 \times 10^{-7} \, \text{ substitute the values into the equation:<br />$E = \frac{(6.626 \times 10^{-34} \, \text{J} \cdot \text{s}) \times (3.00 \times 10^8 \, \text{m/s})}{5.89 \times 10^{-7} \, \text{m}}$<br /><br />Calculating this gives us:<br />$E = 3.36 \times 10^{-19} \, \text{J}$<br /><br />Therefore, the energy of the photons is $3.36 \times 10^{-19} \, \text{J}$.<br /><br />4. Using the same equation as in question 3, we can calculate the energy of the infrared light produced by the electron transition in a hydrogen atom with a wavelength of 746 nm:<br />$E = \frac{(6.626 \times 10^{-34} \, \text{J} \cdot \text{s}) \times (3.00 \times 10^8 \, \text{m/s})}{746 \times 10^{-9} \, \text{m}}$<br /><br />Calculating this gives us:<br />$E = 2.65 \times 10^{-20} \, \text{J}$<br /><br />Therefore, the amount of energy causing this transition is $2.65 \times 10^{-20} \, \text{J}$.<br /><br />5. Using the equation $E = hf$, we can calculate the energy of an x-ray photon with a frequency of $2.4 \times 10^{18} \, \text{s}^{-1}$:<br />$E = (6.626 \times 10^{-34} \, \text{J} \cdot \text{s}) \times (2.4 \times 10^{18} \, \text{s}^{-1})$<br /><br />Calculating this gives us:<br />$E = 1.59 \times 10^{-15} \, \text{J}$<br /><br />Therefore, the energy of the photon is $1.59 \times 10^{-15} \, \text{J}$.<br /><br />6. Using the equation $E = \frac{hc}{\lambda}$, we can calculate the energy of the red light produced by a ruby laser with a wavelength of 500 nm:<br />$E = \frac{(6.626 \times 10^{-34} \, \text{J} \cdot \text{s}) \times (3.00 \times 10^8 \, \text{m/s})}{500 \times 10^{-9, \text{m}}$<br /><br />Calculating this gives us:<br />$E = 3.98 \