The question asks to find the total number of photons emitted by a 100 W yellow lamp with a specific wavelength ($\lambda = 560\text{ nm}$) in 1.0 second, assuming 100% efficiency.

Photon Emission Calculation

We need to determine the number of photons ($N$) using the lamp's power ($P$), the time duration ($t$), the wavelength of light ($\lambda$), Planck's constant ($h$), and the speed of light ($c$).

Step 1: Calculate the energy of a single photon

The energy ($E_{photon}$) of a single photon is given by the formula:

$E_{photon} = \frac{hc}{\lambda}$

Given:

• $h = 6.6 \times 10^{-34}\text{ Js}$
• $c = 3.0 \times 10^8\text{ m s}^{-1}$
• $\lambda = 560\text{ nm} = 560 \times 10^{-9}\text{ m}$

Substitute the values:

$E_{photon} = \frac{(6.6 \times 10^{-34}\text{ Js}) \times (3.0 \times 10^8\text{ m s}^{-1})}{560 \times 10^{-9}\text{ m}}$

$E_{photon} = \frac{19.8 \times 10^{-26}}{560 \times 10^{-9}}\text{ J}$

$E_{photon} \approx 0.035357 \times 10^{-17}\text{ J}$

$E_{photon} \approx 3.5357 \times 10^{-19}\text{ J}$

Step 2: Calculate the total energy emitted by the lamp

The total energy ($E_{total}$) emitted by the lamp in a given time is the product of its power ($P$) and the time duration ($t$).

Given:

• $P = 100\text{ W}$
• $t = 1.0\text{ s}$

$E_{total} = P \times t$

$E_{total} = 100\text{ W} \times 1.0\text{ s} = 100\text{ J}$

Step 3: Calculate the number of photons

The total number of photons ($N$) is the total energy emitted divided by the energy of a single photon.

$N = \frac{E_{total}}{E_{photon}}$

$N = \frac{100\text{ J}}{3.5357 \times 10^{-19}\text{ J}}$

$N \approx 28.28 \times 10^{19}$

$N \approx 2.8 \times 10^{20}$

Therefore, the number of photons emitted by the lamp is approximately $2.8 \times 10^{20}$.