Question

electromagnetic waves carry energy in fixed amounts called quanta. german physicist max planck proposed that the energy of one quantum depends on the frequency of the electromagnetic wave. planck proposed this formula to find the energy of a wave: e = hf each electromagnetic waves energy (e) is proportional to its frequency (f). plancks constant, h, relates energy and frequency and has a value of 6.626 × 10^(-34) joule - seconds (j·s). complete the table to determine the energy carried by each electromagnetic wave traveling in a vacuum. write your answers in scientific notation rounded to two decimal places.

Explanation:

Step1: Calculate energy for radio wave

Use the formula \(E = hf\), where \(h = 6.626\times10^{-34}\space J\cdot s\) and \(f = 4.50\times 10^{7}\space Hz\).
\(E=(6.626\times 10^{-34})\times(4.50\times 10^{7})\)
Using the rule \(a\times10^{m}\times b\times10^{n}=a\times b\times10^{m + n}\), we have \(6.626\times4.50\times10^{-34 + 7}\)
\(6.626\times4.50 = 29.817\), so \(E = 29.817\times10^{-27}=2.98\times10^{-26}\space J\)

Step2: Calculate energy for microwave

Here \(f = 7.93\times 10^{10}\space Hz\)
\(E=(6.626\times 10^{-34})\times(7.93\times 10^{10})\)
\(6.626\times7.93\times10^{-34+10}\)
\(6.626\times7.93 = 52.54418\), so \(E = 52.54418\times10^{-24}=5.25\times10^{-23}\space J\)

Step3: Calculate energy for ultraviolet wave

Here \(f = 2.81\times 10^{16}\space Hz\)
\(E=(6.626\times 10^{-34})\times(2.81\times 10^{16})\)
\(6.626\times2.81\times10^{-34 + 16}\)
\(6.626\times2.81=18.61906\), so \(E = 18.61906\times10^{-18}=1.86\times10^{-17}\space J\)

Answer:

• Radio wave: \(2.98\times 10^{-26}\space J\)
• Microwave: \(5.25\times 10^{-23}\space J\)
• Ultraviolet wave: \(1.86\times 10^{-17}\space J\)