To determine which wave contains the lowest energy, we can use the formula for the energy of a photon, given by:
\[ E = h \cdot f \]
where:
- \( E \) is the energy,
- \( h \) is Planck's constant (approximately \( 6.626 \times 10^{-34} , \text{Js} \)), and
- \( f \) is the frequency of the wave.
Since the energy is directly proportional to frequency, we can simply compare the frequencies of the waves to determine which has the lowest energy.
Here are the frequencies of the waves:
- Wave 1: \( 6.66 \times 10^{14} , \text{Hz} \)
- Wave 2: \( 5.77 \times 10^{14} , \text{Hz} \)
- Wave 3: \( 4.61 \times 10^{14} , \text{Hz} \)
- Wave 4: \( 4.28 \times 10^{14} , \text{Hz} \)
From this list, we can see that Wave 4 has the lowest frequency at \( 4.28 \times 10^{14} , \text{Hz} \), and thus it also contains the lowest energy.
The answer is:
wave 4
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