A light beam from a 2.1-mW He-Ne laser has a wavelength of 633 nm. How many photons does the laser emit in one second? (h = 6.626 × 10-34 J ∙ s, c = 3.00 × 108 m/s)

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BlackTom AI · Accepted Answer

Question restatement: A light beam from a 2.1-mW He-Ne laser with wavelength 633 nm asks for the number of photons emitted per second. Given constants: h = 6.626 × 10^-34 J·s, c = 3.00 × 10^8 m/s.

Option A: 8.8 × 10^15 photons/s. To check, first compute the energy per photon: E = h c / λ = (6.626e-34 J·s)(3.00e8 m/s) / (633e-9 m) ≈ 3.14e-19 J. The photon flux is N = P / E = (2.1e-3 W) / (3.14e-19 J) ≈ 6.69e15 photons/s. Compare this to A: 8.8e15 is larger than our computed value by roughly a factor of 1.3. This suggests A overestimates the true photon rate based on these constants.

Option B: 6.7 × 10^15 photons/s. This matches the calculation above very closely: N ≈ 6.69e15. Since the result is derived directly from dividing the total power by the single-photon energy, B reflects the precise result you would obtain with the given numbers, within rounding.

Option C: 1.1 × 10^16 photons/s. This is about 1.65 times larger than the computed value. The discrepancy could arise from rounding or using a slightly different λ, h, or c, but with the provided values the energy per photon is about 3.14e-19 J, which yields ≈6.7e15 photons/s, not 1.1e16.

Option D: 1.3 × 10^16 photons/s. This is roughly double the computed value. It significantly overestimates the photon rate given the specified constants and wavelength, indicating a larger error than simple rounding.

Detailed calculation check:
- Photon energy: E = h c / λ = (6.626 × 10^-34 J·s)(3.00 × 10^8 m/s) / (633 × 10^-9 m) ≈ 3.14 × 10^-19 J
- Photons per second: N = P / E = (2.1 × 10^-3 W) / (3.14 × 10^-19 J) ≈ 6.69 × 10^15 s^-1
- The closest option to 6.69 × 10^15 is B: 6.7 × 10^15, which aligns with the direct calculation.

Conceptual takeaway: The photon emission rate equals the total power divided by the energy per photon. Any option deviating substantially from this value indicates an incorrect application of the energy-per-photon relation or a mismatch in the constants used. The small differences between closely related numeric options usually come from rounding, but here the computed value clearly points toward a rate around 6.7 × 10^15 photons per second rather than 8.8 × 10^15, 1.1 × 10^16, or 1.3 × 10^16.

A light beam from a 2.1-mW He-Ne laser has a wavelength of 633 nm. How many photons does the laser emit in one second? (h = 6.626 × 10-34 J ∙ s, c = 3.00 × 108 m/s)单项选择题

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