A 100 W sodium lamp radiates energy uniformly in all directions. The lamp is located at the centre of a large sphere that absorbs all the sodium light which is incident on it. The wavelength of the sodium light is 589 nm. At what rate are the photons delivered to the sphere?

Sodium Lamp Photon Emission Rate

Given Data:

• Power of lamp = 100 W = 100 J/s
• Wavelength (λ) = 589 nm = 589 × 10^-9 m
• Planck's constant (h) = 6.626 × 10^-34 J·s
• Speed of light (c) = 3.00 × 10⁸ m/s

Step 1: Calculate Energy of One Photon

The energy of a photon is given by:

E = hc/λ

Substituting values:

E = (6.626 × 10^-34 × 3.00 × 10⁸) / (589 × 10^-9)

E = 1.9878 × 10^-25 / 589 × 10^-9

E ≈ 3.37 × 10^-19 J

Step 2: Calculate Number of Photons per Second

The rate of photon emission is:

n = Power / Energy per photon

n = 100 J/s / 3.37 × 10^-19 J

n ≈ 2.97 × 10²⁰ photons/sec

Final Answer:The rate at which photons are delivered to the sphere is 3.0 × 10²⁰ photons per second.Note: This calculation assumes all the energy is emitted at 589 nm and uniformly distributed in all directions.