Use the information about four different waves to answer the question.
Wave # Frequency Wavelength
Wave 1 6.66 × 1014 Hz 450 nm
Wave 2 5.77 × 1014 Hz 520 nm
Wave 3 4.61 × 1014 Hz 650 nm
Wave 4 4.28 × 1014 Hz 700 nm
Which wave contains the lowest energy?
(1 point)
Responses
wave 2
wave 2
wave 1
wave 1
wave 4
wave 4
wave 3
wave 3
To determine which wave contains the lowest energy, we can consider the relationship between frequency and energy. The higher the frequency of a wave, the greater its energy.
Comparing the frequencies of the given waves:
Wave 1: 6.66 × 10^14 Hz
Wave 2: 5.77 × 10^14 Hz
Wave 3: 4.61 × 10^14 Hz
Wave 4: 4.28 × 10^14 Hz
Since Wave 2 has the highest frequency among the given waves, it also has the highest energy. Therefore, the wave with the lowest energy would be Wave 3, with a frequency of 4.61 × 10^14 Hz.
To determine which wave has the lowest energy, we need to understand the relationship between energy, frequency, and wavelength. The energy of a wave is directly proportional to its frequency and inversely proportional to its wavelength.
The equation that relates these quantities is: E = hf, where E represents energy, h is Planck's constant, and f is the frequency of the wave.
Now, let's analyze the given data:
Wave 1: Frequency = 6.66 × 10^14 Hz, Wavelength = 450 nm
Wave 2: Frequency = 5.77 × 10^14 Hz, Wavelength = 520 nm
Wave 3: Frequency = 4.61 × 10^14 Hz, Wavelength = 650 nm
Wave 4: Frequency = 4.28 × 10^14 Hz, Wavelength = 700 nm
To compare the energy of each wave, we have to express the information in a consistent unit. Let's convert the wavelengths to meters as it is the SI unit for measuring wavelength.
Wave 1: Wavelength = 450 nm = 450 × 10^-9 m
Wave 2: Wavelength = 520 nm = 520 × 10^-9 m
Wave 3: Wavelength = 650 nm = 650 × 10^-9 m
Wave 4: Wavelength = 700 nm = 700 × 10^-9 m
Now, let's calculate the energy for each wave using the equation E = hf:
Wave 1: E1 = (6.66 × 10^14 Hz) · h
Wave 2: E2 = (5.77 × 10^14 Hz) · h
Wave 3: E3 = (4.61 × 10^14 Hz) · h
Wave 4: E4 = (4.28 × 10^14 Hz) · h
Since Planck's constant (h) is a constant value, the wave with the lowest frequency, and thus lowest energy, will have the lowest product when multiplied by h.
Comparing the frequencies, we see that Wave 4 has the lowest frequency (4.28 × 10^14 Hz). Therefore, Wave 4 contains the lowest energy.