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Fundamentals Of Physics
Found in: Page 1182

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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 4.6×1026 photons.

See the step by step solution

Step by Step Solution

Describe the expression of frequency and energy of the photon:

The expression for frequency of photon is given by,

f=cλ ….. (1)

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

The energy of a photon is given by,

E = hf ….. (2)

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

Combine the above two equations.

E=hcλ ….. (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 nm

Plank’s constant, h=6.626×10-34 J·s

The speed of light, c=3×108m/s

Substitute the above values in eq 3.

E = 6.626×10-34 J·s3×108m/s630 nm1m109nm =3.15×10-19 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,

P=93100×60 W=55.8 W

Numberofphotons=power delivered outenergy of each photon =55.8 W3.15×10-19 J =1.77×1020photons/s. =1.77×1020photons/s60smin60minh

Simplify further.

Numberofphotons=6372×1020photons/h =6372×1020 photons/h×730h =4.6×1026 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;" 4.6×1026 photons.

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