An argon ion laser puts out 5.0 W of continuous power at a wavelength of 532 nm. The diameter of the laser beam is 5.5 mm. If the laser is pointed toward a pinhole with a diameter of 1.2 mm, how many photons travel through the pinhole per second? Assume that the light intensity is equally distributed throughout the entire cross-sectional area of the beam. (1 W = 1 J/s)

검증된 단계별 안내

Calculate the energy of a single photon using the formula: \( E = \frac{hc}{\lambda} \), where \( h \) is Planck's constant \( 6.626 \times 10^{-34} \text{ J s} \), \( c \) is the speed of light \( 3.00 \times 10^8 \text{ m/s} \), and \( \lambda \) is the wavelength \( 532 \text{ nm} \) converted to meters.

Determine the cross-sectional area of the laser beam using the formula for the area of a circle: \( A = \pi \left(\frac{d}{2}\right)^2 \), where \( d \) is the diameter of the laser beam \( 5.5 \text{ mm} \) converted to meters.

Calculate the cross-sectional area of the pinhole using the same formula for the area of a circle, with \( d \) as the diameter of the pinhole \( 1.2 \text{ mm} \) converted to meters.

Find the fraction of the laser beam's power that passes through the pinhole by dividing the area of the pinhole by the area of the laser beam.

Calculate the number of photons passing through the pinhole per second by multiplying the total power of the laser \( 5.0 \text{ W} \) by the fraction of power passing through the pinhole, and then dividing by the energy of a single photon.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Photon Energy

The energy of a photon is determined by its wavelength, given by the equation E = hc/λ, where E is energy, h is Planck's constant (6.626 x 10^-34 J·s), c is the speed of light (3.00 x 10^8 m/s), and λ is the wavelength in meters. For a wavelength of 532 nm, this relationship allows us to calculate the energy of each photon emitted by the laser.

Laser Beam Intensity

The intensity of a laser beam is defined as the power per unit area. In this case, the total power output of the laser (5.0 W) is distributed over the cross-sectional area of the beam, which can be calculated using the formula A = π(d/2)², where d is the diameter of the beam. This intensity helps determine how many photons pass through a given area, such as the pinhole.

Photon Flux

Photon flux refers to the number of photons passing through a unit area per unit time. It can be calculated by dividing the intensity of the laser beam by the energy of a single photon. By determining the area of the pinhole and multiplying the photon flux by this area, we can find the total number of photons that travel through the pinhole each second.