Question

A $250$ watt bulb emits monochromatic light of wavelength $198.78$ nm. How many photons are emitted by the bulb per second? \ (Planck’s constant = $6.626 \times 10^{-34}$ J s and velocity of light = $3 \times 10^8$ ms$^{-1}$)

• A. $2.5 \times 10^{20}\text{ s}^{-1}$
• B. $2.5 \times 10^{18}\text{ s}^{-1}$
• C. $2 \times 10^{20}\text{ s}^{-1}$
• D. $2.2 \times 10^{16}\text{ s}^{-1}$
• E. $2.6 \times 10^{20}\text{ s}^{-1}$

Hint:

Number of photons per second = Power ÷ Energy of one photon.

Answer 1

The Correct Option is A

Concept: Physics - Photon Energy. [ E=\frac{hc}{\lambda} ]
Step 1: Convert wavelength into metre. [ \lambda=198.78\text{ nm}=198.78 \times 10^{-9}\text{ m} ]
Step 2: Energy of one photon. [ E=\frac{6.626\times10^{-34}\times3\times10^8}{198.78\times10^{-9}} ] [ E \approx 1\times10^{-18}\text{ J} ]
Step 3: Use power of bulb. Power = energy emitted per second = $250$ J/s [ n=\frac{250}{10^{-18}}=2.5\times10^{20} ]
Step 4: Final answer. [ \boxed{2.5\times10^{20}\text{ photons/s}} ]
Hence, correct option is (A).