Book edition 10th Edition

Author(s) David Halliday

Pages 1328 pages

ISBN 9781118230718

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Short Answer

A special kind of lightbulb emits monochromatic light of wavelength 630 nm. Electrical energy is supplied to it at the rate of 60W, and the bulb is 93% efficient at converting that energy to light energy. How many photons are emitted by the bulb during its lifetime of 730h?

The number of photons are $4.6 \times 10^{26} photons .$

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Describe the expression of frequency and energy of the photon:

The expression for frequency of photon is given by,

$f = \frac{c}{λ}$ ….. (1)

Here, c is the speed of light and $λ$ is the wavelength.

The energy of a photon is given by,

$E = h f$ ….. (2)

Here, h is Planck’s constant and is the frequency.

Combine the above two equations.

$E = \frac{h c}{λ}$ ….. (3)

Determine the number of photons emitted by the bulb during its lifetime of 730h:

Consider the given data as below.

The wavelength, $λ = 630 n m$

Plank’s constant, $h = 6.626 \times 10^{- 34} J \cdot s$

The speed of light, $c =3 \times 10^{8} m / s$

Substitute the above values in eq 3.

$E = \frac{(6.626 \times 10^{- 34} J \cdot s) (3 \times 10^{8} m / s)}{(630 nm) (\frac{1 m}{10^{9} n m})} = 3.15 \times 10^{- 19} J$

Rate at which electrical energy is supplied is 60W. But the bulb is only 93% efficient in converting this energy into light.

The power delivered from the light is,

$\begin{matrix} P = \frac{93}{100} \times 60 W \\ = 55.8 W \end{matrix}$

$Numberofphotons = \frac{power delivered out}{energy of each photon} = \frac{55.8 W}{3.15 \times 10^{- 19} J} = 1.77 \times 10^{20} photons / s . = (1.77 \times 10^{20} photons / s) (\frac{60 s}{\min}) (\frac{60 \min}{h})$

Simplify further.

$Numberofphotons = 6372 \times 10^{20} p h o t o n s / h = 6372 \times 10^{20} p h o t o n s / h \times 730 h = 4.6 \times 10^{26} photons$

Hence, the number of photons arelocalid="1663135942932" style="width:30%" style="width:30%" style="width:30%" style="width:30%" style="max-width: none; vertical-align: -4px;" $4.6 \times 10^{26} photons$ .

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Short Answer

A special kind of lightbulb emits monochromatic light of wavelength 630 nm. Electrical energy is supplied to it at the rate of 60W, and the bulb is 93% efficient at converting that energy to light energy. How many photons are emitted by the bulb during its lifetime of 730h?

Step by Step Solution

Describe the expression of frequency and energy of the photon:

Determine the number of photons emitted by the bulb during its lifetime of 730h:

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Fundamentals Of Physics

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Short Answer

A special kind of lightbulb emits monochromatic light of wavelength 630 nm. Electrical energy is supplied to it at the rate of 60W, and the bulb is 93% efficient at converting that energy to light energy. How many photons are emitted by the bulb during its lifetime of 730h?

Step by Step Solution

Describe the expression of frequency and energy of the photon:

Determine the number of photons emitted by the bulb during its lifetime of 730h:

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