Question

An electric bulb of \(100 \mathrm{w}\) converts \(3 \%\) of electrical energy into light energy. If the wavelength of light emitted is \(6625 \AA\), the number of photons emitted is \(1 \mathrm{~s}\) is \(\ldots \ldots\) $\left(\mathrm{h}=6.625 \times 10^{-34} \mathrm{~J} . \mathrm{s}\right)$ (A) \(10^{17}\) (B) \(10^{19}\) (C) \(10^{21}\) (D) \(10^{15}\)

Short answer

The number of photons emitted in 1 second is \(10^{19}\). The correct answer is (B) \(10^{19}\).

Step-by-step solution

Calculate the light energy emitted by the bulb in 1 second

Given that the bulb converts 3% of electrical energy into light energy, the light energy emitted by the bulb can be calculated as follows: Light energy = (3 / 100) * Power of the bulb * Time Light energy = (3 / 100) * 100 W * 1 s Light energy = 3 J

Find the energy of a single photon

The energy of a single photon can be calculated using the Planck's equation, which is given by: Energy of a photon (E) = Planck's constant (h) * Speed of light (c) / Wavelength (lambda) Given the wavelength (lambda) = 6625 Å = 6625 * 10^{-10} m and Planck's constant (h) = 6.625 * 10^{-34} Js, we can substitute the values in the equation: E = (6.625 * 10^{-34} Js) * (3 * 10^8 m/s) / (6625 * 10^{-10} m) E ≈ 3 * 10^{-19} J

Calculate the number of photons emitted in 1 second

We now have the total light energy emitted by the bulb (3 J) and the energy of a single photon (3 * 10^{-19} J). We can calculate the number of photons emitted in 1 second by dividing the total light energy by the energy of a single photon: Number of photons = Light energy / Energy of a single photon Number of photons = (3 J) / (3 * 10^{-19} J) Number of photons = 10^{19} The correct answer is (B) 10^{19}.