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Chapter 17: Problem 2343

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

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

Step by step solution

01

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
02

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
03

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}.

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Most popular questions from this chapter

Uncertainty in position of electron is found of the order of de-Broglie wavelength. Using Heisenberg's uncertainty principle, it is found that order of uncertainty in its velocity \(=\ldots \ldots \ldots .\) (A) \(1 \mathrm{v}\) (B) \(2 \mathrm{v}\) (C) \((\mathrm{v} / 2 \pi)\) (D) \(2 \pi \mathrm{v}\)

A photon, an electron and a uranium nucleus all have same wavelength. The one with the most energy \(\ldots \ldots \ldots \ldots\) (A) is the photon (B) is the electron (C) is the uranium nucleus (D) depends upon the wavelength and properties of the particle.

\(2 \mathrm{nW}\) light of wave length \(4400 \AA\) is incident on photo sensitive surface of \(\mathrm{Cs}\). If quantum efficiency is \(0.5 \%\), what will be the value of photoelectric current? (A) \(1.56 \times 10^{-6} \mu \mathrm{A}\) (B) \(2.56 \times 10^{-6} \mu \mathrm{A}\) (C) \(4.56 \times 10^{-6} \mu \mathrm{A}\) (D) \(3.56 \times 10^{-6} \mu \mathrm{A}\)

Matching type questions: (Match, Column-I and Column-II property) Column-I Column-II (A) Planck's theory of quantum (p) Light energy \(=\mathrm{hv}\) (B) Einstein's theory of quanta (q) Angular momentum of electron in an orbit. (C) Bohr's stationary orbit (r) Oscillator energies (D) D-Broglie waves (s) Electron microscope (A) \((\mathrm{A}-\mathrm{p}),(\mathrm{b}-\mathrm{q}),(\mathrm{C}-\mathrm{r}),(\mathrm{D}-\mathrm{s})\) (B) \((\mathrm{A}-\mathrm{q}),(\mathrm{B}-\mathrm{r}),(\mathrm{C}-\mathrm{s}),(\mathrm{D}-\mathrm{p})\) (C) \((\mathrm{A}-\mathrm{r}),(\mathrm{B}-\mathrm{p}),(\mathrm{C}-\mathrm{q}),(\mathrm{D}-\mathrm{s})\) (D) \((\mathrm{A}-\mathrm{r}),(\mathrm{B}-\mathrm{p}),(\mathrm{C}-\mathrm{s}),(\mathrm{D}-\mathrm{q})\)

Each of the following questions contains statement given in two columns, which have to be matched. The answers to these questions have to be appropriately dubbed. If the correct matches are $\mathrm{A}-\mathrm{q}, \mathrm{s}, \mathrm{B}-\mathrm{p}, \mathrm{r}, \mathrm{C}-\mathrm{q}, \mathrm{s}$ and \(\mathrm{D}-\mathrm{s}\) then the correctly dabbled matrix will look like the one shown here: Match the statements of column I with that of column II. Column-I Column-II (A) \(\propto\) -particle and proton have same \(\mathrm{K} . \mathrm{E}\). \((\mathrm{p}) \lambda_{\mathrm{p}}=\lambda_{\propto}\) (B) \(\propto\) -particle has one quarter \(\mathrm{K} . \mathrm{E}<\) than that (q) \(\lambda_{\mathrm{p}}>\lambda_{\propto}\) (C) proton has one quarter \(\mathrm{K} . \mathrm{E}\). than that (r) \(p_{p}=p_{\propto}\) (D) \(\propto\) -particle and proton same velocity (s) \(\mathrm{p}_{\propto}>\mathrm{p}_{\mathrm{p}}\)
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