7. What is the frequency of UV light that has an energy of 2.39times 10^-18J i 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

7. To find the frequency of UV light with an energy of $2.39\times 10^{-18}J$, we can use the formula $E = hf$, where $E$ is the energy, $h$ is Planck's constant ($6.626\times 10^{-34}J\cdot s$), and $f$ is the frequency. Rearranging the formula, we get $f = \frac{E}{h}$. Plugging in the given values, we have $f = \frac{2.39\times 10^{-18}J}{6.626\times 10^{-34}J\cdot s} \approx 3.61\times 10^{15}Hz$.<br /><br />8. To find the wavelength and frequency of photons with an energy of $1.4\times 10^{-21}J$, we can use the same formula $E = hf$. Rearranging the formula, we get $f = \frac{E}{h}$. Plugging in the given values, we have $f = \frac{1.4\times 10^{-21}J}{6.626\times 10^{-34}J\cdot s} \approx 2.11\times 10^{12}Hz$. To find the wavelength, we can use the formula $c = \lambda f$, where $c$ is the speed of light ($3.00\times 10^8m/s$) and $\lambda$ is the wavelength. Rearranging the formula, we get $\lambda = \frac{c}{f}$. Plugging in the values, we have $\lambda = \frac{3.00\times 10^8m/s}{2.11\times 10^{12}Hz} \approx 1.42\times 10^{-4}m$ or 142 nm.<br /><br />9. To find the energy of light with a wavelength of 434 nm, we can use the formula $E = \frac{hc}{\lambda}$, where $h$ is Planck's constant, $c$ is the speed of light, and $\lambda$ is the wavelength. Plugging in the given values, we have $E = \frac{(6.626\times 10^{-34}J\cdot s)(3.00\times 10^8m/s)}{434\times 10^{-9}m} \approx 4.56\times 10^{-19}J$.<br /><br />10. To find the wavelength of light with a frequency of $3.42\times 10^{11}Hz$, we can use the formula $\lambda = \frac{c}{f}$, where $c$ is the speed of light and $f$ is the frequency. Plugging in the given values, we have $\lambda = \frac{3.00\times 10^8m/s}{3.42\times 10^{11}Hz} \approx 8.77\times 10^{-3}m$ or 877 nm.