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The table below shows the wavelength of four electromagnetic waves in meters [tex]\((m)\)[/tex].

\begin{tabular}{|c|c|}
\hline
Electromagnetic Wave & Wavelength \\
\hline
A & [tex]\(3.0 \times 10^2 \, m\)[/tex] \\
\hline
B & [tex]\(4.0 \times 10^{-6} \, m\)[/tex] \\
\hline
C & [tex]\(1.2 \times 10^{-12} \, m\)[/tex] \\
\hline
D & [tex]\(2.0 \times 10^{-9} \, m\)[/tex] \\
\hline
\end{tabular}

According to the table, which electromagnetic wave has the least amount of energy?

A. A

B. B

C. C

D. D

Sagot :

To determine which electromagnetic wave has the least amount of energy, we need to use the relationship between the energy of a wave ([tex]\(E\)[/tex]) and its wavelength ([tex]\(\lambda\)[/tex]). The formula connecting these two quantities is given by:

[tex]\[ E = \frac{hc}{\lambda} \][/tex]

where:
- [tex]\(h\)[/tex] is Planck's constant ([tex]\(6.62607015 \times 10^{-34}\)[/tex] Joule-seconds),
- [tex]\(c\)[/tex] is the speed of light in a vacuum ([tex]\(3 \times 10^8\)[/tex] meters per second),
- [tex]\(\lambda\)[/tex] is the wavelength.

Using this formula, we can calculate the energy for each of the waves A, B, C, and D. Here are the steps:

1. Wave A:
[tex]\[ \lambda_A = 3.0 \times 10^2 \, \text{m} \][/tex]
[tex]\[ E_A = \frac{6.62607015 \times 10^{-34} \times 3 \times 10^8}{3.0 \times 10^2} \][/tex]
[tex]\[ E_A = 6.62607015 \times 10^{-28} \, \text{J} \][/tex]

2. Wave B:
[tex]\[ \lambda_B = 4.0 \times 10^{-6} \, \text{m} \][/tex]
[tex]\[ E_B = \frac{6.62607015 \times 10^{-34} \times 3 \times 10^8}{4.0 \times 10^{-6}} \][/tex]
[tex]\[ E_B = 4.9695526125 \times 10^{-20} \, \text{J} \][/tex]

3. Wave C:
[tex]\[ \lambda_C = 1.2 \times 10^{-12} \, \text{m} \][/tex]
[tex]\[ E_C = \frac{6.62607015 \times 10^{-34} \times 3 \times 10^8}{1.2 \times 10^{-12}} \][/tex]
[tex]\[ E_C = 1.6565175375 \times 10^{-13} \, \text{J} \][/tex]

4. Wave D:
[tex]\[ \lambda_D = 2.0 \times 10^{-9} \, \text{m} \][/tex]
[tex]\[ E_D = \frac{6.62607015 \times 10^{-34} \times 3 \times 10^8}{2.0 \times 10^{-9}} \][/tex]
[tex]\[ E_D = 9.939105225 \times 10^{-17} \, \text{J} \][/tex]

From the calculated energies, we have:
- Energy [tex]\(E_A = 6.62607015 \times 10^{-28} \, \text{J}\)[/tex]
- Energy [tex]\(E_B = 4.9695526125 \times 10^{-20} \, \text{J}\)[/tex]
- Energy [tex]\(E_C = 1.6565175375 \times 10^{-13} \, \text{J}\)[/tex]
- Energy [tex]\(E_D = 9.939105225 \times 10^{-17} \, \text{J}\)[/tex]

Comparing these values, the wave with the least amount of energy is Wave A with energy [tex]\(E_A = 6.62607015 \times 10^{-28} \, \text{J}\)[/tex].

Therefore, the electromagnetic wave with the least amount of energy is Wave A.