A microwave has a frequency of 90 GHz, which is the same as \( 9.0 \times 10^{10} \mathrm{~Hz} \). What is the energy of electromagnetic radiation from the microwave? \( \mathrm{h}=6.626 \times 10^{-34} \mathrm{~J} \cdot \mathrm{~s} \) \( [?] \times 10^{[?]} \mathrm{J} \)

To find the energy of electromagnetic radiation from the microwave, we can use the formula: \[ E = h \cdot f \] 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 (\( 9.0 \times 10^{10} \, \text{Hz} \)). Substituting the values: \[ E = (6.626 \times 10^{-34} \, \text{J} \cdot \text{s}) \times (9.0 \times 10^{10} \, \text{Hz}) \] Calculating this gives: \[ E = 5.9634 \times 10^{-23} \, \text{J} \] So, rounding it appropriately, the energy of electromagnetic radiation from the microwave is approximately: \[ 5.96 \times 10^{-23} \, \text{J} \] The answer can be written as \( 5.96 \times 10^{-23} \). To match your desired output: \( 5.96 \times 10^{-23} \mathrm{~J} \) --- It's fascinating to consider that the microwaves we cook our food with are the same type of energy waves that power our Wi-Fi and mobile networks! The frequencies that allow microwave ovens to heat food also play a crucial role in communication technology, seamlessly blending food-making with information sharing. Microwaves have a key role in everyday life, but some common mistakes when using them include not covering food, leading to splatters and uneven heating. Always use a microwave-safe container to prevent unwanted reactions between materials and the microwave's heating process!