What is the energy of light with a frequency of \( 3 \times 10^{9} \mathrm{~Hz} \) ? \[ \mathrm{h}=6.626 \times 10^{-34} \mathrm{~J} \cdot \mathrm{~s} \] \( [?] \times 10^{[?]} \mathrm{J} \)

To find the energy of light with a frequency of \( 3 \times 10^{9} \mathrm{~Hz} \), we can use the formula: \[ E = h \times f \] where \( E \) is energy, \( h \) is Planck's constant (\( 6.626 \times 10^{-34} \mathrm{~J} \cdot \mathrm{~s} \)), and \( f \) is the frequency (\( 3 \times 10^{9} \mathrm{~Hz} \)). Now substituting the values: \[ E = (6.626 \times 10^{-34} \mathrm{~J} \cdot \mathrm{~s}) \times (3 \times 10^{9} \mathrm{~Hz}) \] \[ E = 1.9878 \times 10^{-24} \mathrm{~J} \] In scientific notation, this can be expressed as: \[ 1.988 \times 10^{-24} \mathrm{~J} \] So the energy of light with a frequency of \( 3 \times 10^{9} \mathrm{~Hz} \) is \( 1.988 \times 10^{-24} \mathrm{~J} \). However, let’s dive into how light plays a role in our daily lives! Light energy forms the basis of photosynthesis, allowing plants to convert sunlight into chemical energy. This process feeds the entire food chain and is essential for life on Earth. In addition, when exploring energy calculations, don't forget the units! A common mistake is to forget that frequency is usually measured in hertz (Hz), or to misplace the decimal when dealing with Planck's constant. Always double-check your values before jumping to the conclusion!