Question

a radio station broadcasts on a frequency of 103.7 mhz, which is the same as 1.037×10^8 hz. what is the energy of the radio wave?
h = 6.626×10^(-34) j·s
?×10^? j

Explanation:

Step1: Recall the energy - frequency formula

The energy of a photon (or in this case, a radio - wave photon) is given by the formula $E = hf$, where $E$ is the energy, $h$ is Planck's constant, and $f$ is the frequency.

Step2: Substitute the given values

We are given that $h = 6.626\times10^{-34}\ J\cdot s$ and $f=1.037\times 10^{8}\ Hz$.
$E=(6.626\times 10^{-34}\ J\cdot s)\times(1.037\times 10^{8}\ Hz)$

Step3: Use the rule of exponents for multiplication

When multiplying numbers in scientific notation $a\times10^{m}$ and $b\times10^{n}$, we use the formula $(a\times10^{m})\times(b\times10^{n})=(a\times b)\times10^{m + n}$.
$E=(6.626\times1.037)\times10^{-34 + 8}\ J$
$6.626\times1.037 = 6.871162$
$E = 6.871162\times10^{-26}\ J$

Answer:

$6.87\times 10^{-26}\ J$