Question

Maximum number of photons emitted by a bulb capable of producing monochromatic light of wavelength 550 nm is ______, if 100 V and 1 A is supplied for one hour.

• A. $1 \times 10^{24}$
• B. $5 \times 10^{24}$
• C. $1 \times 10^{23}$
• D. $5 \times 10^{23}$
• E. $5 \times 10^{22}$

Hint:

When converting time for energy calculations, always use seconds. The relationship $E = nhc/\lambda$ is central to problems involving light intensity and photon counts.

Answer 1

The Correct Option is A

Concept: The total energy supplied by an electrical source is $E = V \cdot I \cdot t$. This energy is equal to the total energy of $n$ photons, where the energy of one photon is $E_{photon} = \frac{hc}{\lambda}$.

Step 1: {Calculate total electrical energy supplied.}
Voltage ($V$) = $100 \text{ V}$, Current ($I$) = $1 \text{ A}$, Time ($t$) = $1 \text{ hour} = 3600 \text{ s}$. $$E_{total} = 100 \times 1 \times 3600 = 3.6 \times 10^5 \text{ J}$$

Step 2: {Calculate the energy of a single photon.}
Wavelength ($\lambda$) = $550 \text{ nm} = 550 \times 10^{-9} \text{ m}$. $$E_{photon} = \frac{hc}{\lambda} = \frac{6.626 \times 10^{-34} \times 3 \times 10^8}{550 \times 10^{-9}} \approx 3.6 \times 10^{-19} \text{ J}$$

Step 3: {Calculate the number of photons (n).}
$$n = \frac{E_{total}}{E_{photon}} = \frac{3.6 \times 10^5}{3.6 \times 10^{-19}}$$ $$n = 10^{24} = 1 \times 10^{24}$$