One watt (W) is equal to 1 J/s. Assume that 5.0% of the energy output of a 75 wa

Question

One watt (W) is equal to 1 J/s. Assume that 5.0% of the energy output of a 75 watt light bulb is visible light and that the average wavelength of the light is 550 nm, how many photons per second are emitted by the light bulb? If 5.9 % of the energy of a 75 watt light bulb is visible light, then the rate of energy of all the photons emitted is __________ J/s. (3 significant figures). 1 550 nm wavelength is the same at _________ meters (2 significant figures). One photon with a wavelength of 550 nm has _________ J (2 significant figures) of energy. The rate of photons emitted by the light bulb is _______ photons per second (2 significant figures). (Use E to express powers of 10, e.g. 6.02x10 23 entered as 6.02E23

Explanation / Answer

Assume that 5.0% of the energy output of a 75 watt light bulb is visible light

Total energy = 75 x 5/100 = 3.75 watt light is visible light

One watt (W) is equal to 1 J/s

So, 3.75 watt = 3.75 J/s

Energy carried by one 550nm photon –

Use the relation between energy and wavelength

E photon = h c / lambda

= (6.63 x E-34 J s) x (3.00 x E8 m/s)/ 550 x E-9 m

= 3.62 x E-19 J

So how many of these photons will we need to make 3.5 Joules?

Let's assume we need some number N of them. Then,

3.5 Joules = N x 3.62 x E-19 J

N = 3.5 J / 3.62 x E-19 J

   = 9.67 x E18

So, in order to emit 3.5 Joules per second, the lightbulb must emit 9.67 x E18 photons per second

If 5.9 % of the energy of 75 watt light is visible light

Total energy = 75 x 5.9/100 = 4.43 watt light is visible light

4.43 watt = 4.43 J/s

So how many of these photons will we need to make 4.43 Joules?

Let's assume we need some number N of them. Then,

4.43 Joules = N x 3.62 x E-19 J

N = 4.3 J / 3.62 x E-19 J = 1.19E19

So, in order to emit 4.43 Joules per second, the lightbulb must emit 1.19 x E19 photons per second

If 5.9 % of the energy of a 75 watt light bulb is visible light, then the rate of energy of all the photons emitted is 4.43 J/s. (3 significant figures). 1 550 nm wavelength is the same at 1.6E6 meters (2 significant figures). One photon with a wavelength of 550 nm has 3.6 x E-19 J (2 significant figures) of energy. The rate of photons emitted by the light bulb is 1.2 x E19 photons per second (2 significant figures).

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