To calculate the energy of a wavelength, you can use the equation:
\[ E = \dfrac{hc}{\lambda} \]
Where:
- \( E \) = energy
- \( h \) = Planck's constant (\(6.626 × 10^{-34} \, \text{J s}\))
- \( c \) = speed of light in a vacuum (\(3.00 × 10^8 \, \text{m/s}\))
- \( \lambda \) = wavelength
First, convert the given wavelength from nanometers (nm) to meters (m):
\[ 150 \, \text{nm} = 150 \times 10^{-9} \, \text{m} \]
Now, plug the values into the formula:
\[ E = \dfrac{(6.626 × 10^{-34} \, \text{J s}) \times (3.00 × 10^8 \, \text{m/s})}{150 \times 10^{-9} \, \text{m}} \]
\[ E = \dfrac{1.9888 × 10^{-25} \, \text{J m}}{150 \times 10^{-9} \, \text{m}} \]
\[ E \approx 1.3252 × 10^{-16} \, \text{J} \]
Therefore, the energy of a wavelength of 150. nm is approximately \(1.3252 × 10^{-16}\) joules.