Chapter 38: Q4P (page 1181)

A helium–neon laser emits red light at wavelength $λ = 633 n m$ in a beam of diameter 3.5 mm and at an energy-emission rate of 5.0 mW. A detector in the beam’s path totally absorbs the beam. At what rate per unit area does the detector absorb photons?

Short Answer

Expert verified

The rate of absorption of photon per unit area is $1.7 \times 10^{21} photons / m^{2} . s$

Step by step solution

Describe the expression of energy of the photon

The energy Eof a photon of wavelength $λ$ is given by,

$E = \frac{h c}{λ}$

Here, h is the Planck’s constant, and c is the speed of light.

Determine the rate of absorption of photon per unit area

Assume that the protons are emitted by a rate R from the sodium lamp. Then, the power P of the sodium lamp is equal to the product of rate R and the energy of each photon E.

$\begin{matrix} P = R E \\ P = R (\frac{h c}{λ}) \\ R = \frac{p λ}{h c} \end{matrix}$ …… (1)

Divide the rate R by area of the beam.

$\begin{matrix} \frac{R}{A} = \frac{P λ}{h c \times \frac{π}{4} d^{2}} \\ = \frac{4 P λ}{π d^{2} h c} \end{matrix}$ …… (2)

Therefore, the rate of absorption of photon per unit area is ${1.7×10}^{21} photons / m^{2} . s$

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A helium–neon laser emits red light at wavelength $λ = 633 n m$ in a beam of diameter 3.5 mm and at an energy-emission rate of 5.0 mW. A detector in the beam’s path totally absorbs the beam. At what rate per unit area does the detector absorb photons?

Short Answer

Step by step solution

Describe the expression of energy of the photon

Determine the rate of absorption of photon per unit area

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A helium–neon laser emits red light at wavelength λ=633nmin a beam of diameter 3.5 mm and at an energy-emission rate of 5.0 mW. A detector in the beam’s path totally absorbs the beam. At what rate per unit area does the detector absorb photons?

Short Answer

Step by step solution

Describe the expression of energy of the photon

Determine the rate of absorption of photon per unit area

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Fields in Physics

Modern Physics

Medical Physics

Turning Points in Physics

Particle Model of Matter

Wave Optics

Study anywhere. Anytime. Across all devices.

A helium–neon laser emits red light at wavelength $λ = 633 n m$ in a beam of diameter 3.5 mm and at an energy-emission rate of 5.0 mW. A detector in the beam’s path totally absorbs the beam. At what rate per unit area does the detector absorb photons?