Asodium lamp emits light at the power p = 70.0 w and at the wavelength λ = 600 nm, and the emission is uniformly in all directions.

(a) at what rate are photons emitted by the lamp?

(b) at what distance from the lamp will a totally absorbing screen absorb photons at the rate of 1.00 photon /cm2s?

(c) what is the rate per square meter at which photons are intercepted by a screen at a distance of 1.90 m from the lamp?

a)  # = 21,116 10¹⁹ photons , b)  R = 4,099 10⁷ m , c)  I = 4.66 10¹⁸ photons / m²

Explanation:

a) In this problem we need to know the energy of each photon and the total emitted power

Let's start with the Planck equation

     E = h f

     c =λ f

     E = h c / λ

     E = 6.63 10⁻³⁴ 3 10⁸/600 10⁻⁹

     E = 3,315 10⁻¹⁹ J

This is the energy of a photon

The definition of power is

       P = W / t

Work is equal to energy change

        P = E / t

       E = 70.0  1

        = 70 J

This is the total energy emitted

Let's use a rule of proportions to find the number of photons

       # = / E

       # = 70 / 3,315 10⁻¹⁹

       # = 21,116 10¹⁹ photons

b) The definition of intensity is

       I = P / A

       P = I A

We want an intensity  

        I = 1 photon / cm²

The area of a sphere is

        A = 4π r²

        P = I 4π R²

        R = √ P / 4π I

The power is equal to the number of photons per energy of each photon emitted per unit of time

      R = √ (# / 4π I)

Intensity is

      I = 1 photon / cm² (100 cm / 1m) 2 = 1 10⁴ photon / m²

     R = √ (21,116 10¹⁹ / 4π 10⁴)

     R = √ (16.80 10¹⁴)

     R = 4,099 10⁷ m

c) we calculate the intensity

      A = 4π R²

      A = 4π 1.9²

      A = 45.36 m²

       I = P / A

       I = 21,116 10¹⁹ / 45.36

       I = 4.66 10¹⁸ photons / m²

the order for strong to weak forces such as

strong nuclear force → electromegnetic force → weak nuclear force → gravitational force

the fundamental forces are those forces that act between to objects or element to make interactions. there are four types of fundamental forces such as strong and weak nuclear forces (due to protons and electrons), electromagnetic force (due to the motion of electrons) and gravitational force (due to orbital movement of the planet). if these forces are arranged on the basis of their maximum strength then the order is

strong nuclear force → electromegnetic force → weak nuclear force → gravitational force