A 10W emitter emits monochromatic radiation with a wavelength of 662nm. Determine how many photons this source emits per second. What is the mass of each photon?
N = 10 W.
λ = 662 nm = 662 * 10 ^ -9 m.
c = 3 * 10 ^ 8 m / s.
h = 6.6 * 10 ^ -34 J * s.
t = 1 s.
Power N is the ratio of work A to the time t during which this work is performed.
N = A / t.
Work A = E.
The radiation energy is determined by the formula: E = nph * Eph, where nph is the number of photons, Eph is the energy of one photon.
The energy of one photon is determined by the formula: Ef = h * s / λ. Where h is Planck’s constant, c is the speed of light, λ is the wavelength of the photon.
N = nph * h * s / λ * t.
nph = N * λ * t / h * s.
nph = 10 W * 662 * 10 ^ -9 m * 1 s / 6.6 * 10 ^ -34 J * s * 3 * 10 ^ 8 m / s = 334.3 * 10 ^ 17.
The energy of a photon can also be expressed through the formula: Eph = mph * c ^ 2, where mph is the mass of the photon, c is the speed of the photon (the speed of light).
mph * c ^ 2 = h * c / λ.
mph = h / s * λ.
mph = 6.6 * 10 ^ -34 J * s / 3 * 10 ^ 8 m / s * 662 * 10 ^ -9 m = 3.3 * 10 ^ -36 kg.
Answer: nph = 334.3 * 10 ^ 17, mph = 3.3 * 10 ^ -36 kg.
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