A wave with a frequency of 500 Hz is traveling at a speed of 200 m/s. What is the wavelength ?
1 answer:
The wavelength of the wave is 0.40 m.
Frequency <em>f </em>of a wave is defined as the number of waves traveling through a point in one second. Wavelength λ is the distance traveled by the wave in one complete time period. The speed of the wave <em>v</em> is related to frequency and wavelength by the expression,
Therefore,
Substitute 200 m/s for <em>v</em> and 500 Hz for <em>f</em>.
Thus, the wavelength of the wave is 0.40 m
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Planck's equation states that
E = hf
where
E = the energy,
h = Planck's constant
f = the frequency
Because
c = fλ
where
c = velocity of light,
λ = wavelength
therefore
E = h(c/λ)
Photon #1:
The wavelength is λ₁ = 60 nm.
The energy is
E₁ = (hc)/λ₁
Photon #2:
The energy is twice that of photon #1, therefore its energy is
E₂ = 2E₁ = (hc)/λ₂.
Therefore
Answer: 30 nm
E = hf
where
E = the energy,
h = Planck's constant
f = the frequency
Because
c = fλ
where
c = velocity of light,
λ = wavelength
therefore
E = h(c/λ)
Photon #1:
The wavelength is λ₁ = 60 nm.
The energy is
E₁ = (hc)/λ₁
Photon #2:
The energy is twice that of photon #1, therefore its energy is
E₂ = 2E₁ = (hc)/λ₂.
Therefore
Answer: 30 nm