A radio station broadcasts on a requency of 103.7 MHz which is the same as \( 1.037 \times 10^{8} \mathrm{~Hz} \). What is the energy of the radio wave? \[ \mathrm{h}=6.626 \times 10^{-34} \mathrm{~J} \cdot \mathrm{~s} \] [?] \( ] \times 10^{[?]} \mathrm{J} \)

To find the energy of a radio wave, we can use the formula: \[ E = h \cdot f \] where \( E \) is the energy in joules, \( h \) is Planck's constant (approximately \( 6.626 \times 10^{-34} \, \text{J·s} \)), and \( f \) is the frequency in hertz (which is \( 1.037 \times 10^{8} \, \text{Hz} \) in this case). Substituting the values into the equation, we have: \[ E = (6.626 \times 10^{-34} \, \text{J·s}) \times (1.037 \times 10^{8} \, \text{Hz}) \] Calculating this gives: \[ E \approx 6.87 \times 10^{-26} \, \text{J} \] So, the energy of the radio wave is approximately \( 6.87 \times 10^{-26} \, \text{J} \). Isn't it fascinating that even though radio waves have low energy compared to visible light, they can still carry music and information far and wide? Radio waves make up a vital part of our daily lives, enabling communication, broadcasting, and even remote controls! If you're curious about delving deeper, consider exploring the electromagnetic spectrum, which includes everything from gamma rays to radio waves. Each type of wave has unique properties and applications, making it a captivating topic in physics and engineering!