# Questions related to waves.

by _Mayday_
Tags: waves
 P: 816 Hey, I'm having a few problems with the questions below, now I think alot of it is to do with not knowing how to approach the question. Please forgive me if there is not alot of working out, but I may just need to directing in the right direction. Question 1 The average wavelength of light emitted from an incandescent torch bulb with a metal filament is 120nm. Calculate the number of photons emitted by a 20W torch bulb in one hour. Answer 1 Photon energy is proportional to the frequency of the wave. $$v=f\lambda$$ $$3\times10^8 = f\times 120nm$$ $$\frac{3\times10^8}{120\times10^{-9} = f$$ $$f=2.5\times10^{15}$$ I have the frequency now, but how do I get from here to finding how much is emitted by a 20W torch bulb in 1 hour? Question 2 A photon has a momentum given E/c where E is the enerrgy of the photon and c is the speed of light. If the torch bulb emits parallel beam light, then calculate the force on the torch. Answer 2 I have no idea, at all. I am not asking for the answer, but could someone please direct me in the direction of a method of some sort, even if it is only the intial stages. Question 3 Calculate the initial acceleration of the toch if it was in empty space, and it had a mass of 200g. Answer 3 Again, not idea. I know I have the mass, but that is the only value I have. It could be possible that I need values from previous questions above. I apologise for th elack of working, but the whole thing has me stumped. I know it is against PF regulations to just dish out the answers, but I am willing to work through it, all I need is a gentle push in the right direction! Any help is much appreciated. _Mayday_
 Sci Advisor HW Helper P: 4,738 for Q#1 -What is the relation between power(measured in watts: W), energy and time? -How is the energy of a photon related to its wavelenght / frequency? for Q#2 - Find the relation between linear momentum and force using the definition of linear momentum and Newtons second law. for Q#3 - Do Q#2 first
 P: 816 Q1 A watt is 1 joule of energy per second. The energy of a photon is proportional to it's frequency. If E is constant, then an increase in frequency will result in a decrease in wavelength. I would be able to convert to W now, but it the convertion to Joules in which I am struggling with.
 Sci Advisor HW Helper P: 4,738 Questions related to waves. So how can anyone help you if you are not showing what you did? And WHAT are you trying to convert to Joules? have you seen this formula: $$E_{\gamma} = hf = hc/\lambda$$ ?
P: 816
 Quote by malawi_glenn So how can anyone help you if you are not showing what you did? And WHAT are you trying to convert to Joules? have you seen this formula: $$E_{\gamma} = hf = hc/\lambda$$ ?
I have shown you everything I know how to do. For question 1, I would have thought I would get an answer in Joules, and then convert to Watts.

I have not seen $$E_{\gamma} = hf = hc/\lambda$$ but I have seen $$E_{\gamma} = hf$$

The thing is, I have not used either in school and it is not in the curriculum. If that equation can be used, then I will use it, but I am not sure if there might be an easier way. I will use this one, if you say it will work then.

$$E_{\gamma} = hf = hc/\lambda$$
$$E_{\gamma} = 2.5\times10^{15}h = \frac{3\times10^8h}{120\times10{-9}}$$

I have looked up Planck's Constant and I will use $$6.6\times 10^{-34}$$ as the value.

$$E_{\gamma} = 2.5\times10^{15}h = \frac{3\times10^8h}{120\times10{-9}}$$

$$E_{\gamma} = 2.5\times10^{15}\times 6.6\times10^{-34}=\frac{3\times10^8\times6.6\times10^{-34}}{120\times10{-9}$$

$$E_{\gamma} = 1.65\times10{-18} Joules/s$$

If this is correct then I would multiply my answer by 3600, to get to Hours.
 Sci Advisor HW Helper P: 4,738 check the units of $$E_{\gamma}$$.... Joules/s is totaly madness! Why not just calculate how much energy the torch bulb emits under 1h, and then evaluate the number of photons with wavelength 120nm that energy corresponds to?
 P: 816 I have no idea on the units, planck's constant is in $$m^2 kg / s$$ How do I convert this to J/s?? I think I will do it this way Malawi, the other way will be explained in class but atleast now, I know another method. I am unsue on how to convert my asnwer to J/s.
 Sci Advisor HW Helper P: 4,738 But the units of Energy is J, then you can't get an answer with J/s: $$E_{\gamma} = 1.65\times10{-18} Joules/s$$ As you wrote. This also helps: m^2 kg/s = J*s (from Newtons second law and the fact that 1J = 1N*m) The way you do it is wrong, why not do it the correct way which is the one I told you? "Calculate the number of photons emitted by a 20W torch bulb in one hour." The energy relased by the buld in 1h is 20*3600J, right? One photon with wavelenght 120nm has energy hc/lamda = 6.626*10^-34[Js]*3*10^8(m/s) / (120*10-^9(m)) = 1.655*10^-18J (pretty much as you got, but you got wrong units).
 P: 816 I follow that now. I have a total energy of 72000 Joules One photon has an energy of $$4.35\times10^-8$$ Therefor, the total number of photons must be $$\frac{72000}{4.35\times10^-8} = 4.35\times10^{12}[tex] Thank you for your help here, Malawi. My teacher has not shown us the first equation, and so I do not know how he expected us to do it, other than to do some research. Q2 I can now find the momentum of the photon as I have both E and C. [tex]\frac{1.65\times10^{-18}{3\times10^8} = 5.52\times10^{-27}$$ Now you mentioned Newton's Second law, F=ma. I know that there is an equation that is closely related to this one. EDIT: Thank you for all your time Malawi
 P: 816 I can find the momentum as I have both E and c, so I can do E/c
 P: 816 Okay, I am going to also use information from question 1 to answer this question. Momentum = Force x Time Force = Momentum/Time 1 Hour = 3600 Seconds E/c = $$5.5\times106{-17}$$ $$Force= \frac{5.5\times10{-17}}{3600s}$$ $$Force = 1.52 \times10^{-20}N$$ I don't know if that is any good...
 Sci Advisor HW Helper P: 4,738 no force = time derivative of momentum You cant GATHER force, force is instanteous. So if the bulb casts away 20W photons in the same direction (we was to assue it was a paralell beam), then how can you relate the power of the bulb to the time derivative of momentum, if momenutm = E/c ? btw the energy of one photon is 1.655*10^-18 J
 Sci Advisor HW Helper P: 4,738 maybe this can help you further: Force: $$F = \frac{dp}{dt}$$ units: N Momentum: $$p=E/c$$ units: m*kg/s Power: $$P = \frac{dE}{dt}$$ units: W = J/s = N*m/s
 P: 816 Malawi, I really have no idea at all!!