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. [tex]v=f\lambda[/tex] [tex]3\times10^8 = f\times 120nm[/tex] [tex]\frac{3\times10^8}{120\times10^{-9} = f[/tex] [tex]f=2.5\times10^{15}[/tex] 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_
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
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.
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: [tex] E_{\gamma} = hf = hc/\lambda [/tex] ?
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 [tex] E_{\gamma} = hf = hc/\lambda [/tex] but I have seen [tex]E_{\gamma} = hf[/tex] 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. [tex] E_{\gamma} = hf = hc/\lambda [/tex] [tex] E_{\gamma} = 2.5\times10^{15}h = \frac{3\times10^8h}{120\times10{-9}}[/tex] I have looked up Planck's Constant and I will use [tex]6.6\times 10^{-34}[/tex] as the value. [tex] E_{\gamma} = 2.5\times10^{15}h = \frac{3\times10^8h}{120\times10{-9}}[/tex] [tex] E_{\gamma} = 2.5\times10^{15}\times 6.6\times10^{-34}=\frac{3\times10^8\times6.6\times10^{-34}}{120\times10{-9}[/tex] [tex] E_{\gamma} = 1.65\times10{-18} Joules/s[/tex] If this is correct then I would multiply my answer by 3600, to get to Hours.
check the units of [tex] E_{\gamma} [/tex].... 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?
I have no idea on the units, planck's constant is in [tex]m^2 kg / s[/tex] 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.
But the units of Energy is J, then you can't get an answer with J/s: [tex] E_{\gamma} = 1.65\times10{-18} Joules/s[/tex] 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).
I follow that now. I have a total energy of 72000 Joules One photon has an energy of [tex]4.35\times10^-8[/tex] Therefor, the total number of photons must be [tex]\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}[/tex] 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
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 = [tex]5.5\times106{-17}[/tex] [tex]Force= \frac{5.5\times10{-17}}{3600s}[/tex] [tex]Force = 1.52 \times10^{-20}N[/tex] I don't know if that is any good...
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
maybe this can help you further: Force: [tex] F = \frac{dp}{dt} [/tex] units: N Momentum: [tex] p=E/c [/tex] units: m*kg/s Power: [tex] P = \frac{dE}{dt} [/tex] units: W = J/s = N*m/s
ok, so you are given power and energy. c is just a constant. can you atleast try to relate the known variables with the equations I just gave you?
Students around the world are confused because they don't follow the right sequence. * Convert all givens to SI units. * List all formulas. * Solve algebraically for the unknown without using any numbers. * Sustitute all numbers at once, use your calculator one time. * Check units. Following that sequence, see how easy it is: Givens, converted to SI: power: P= 20W wavelength: lambda = 120 nm = 120X10^-9 m time: t = 1 hr = (1 hr)(60 min / 1 hr)(60 s / 1 min) = 3600 s Equations: energy and power: E=Pt energy of a photon: E=hf=hc/lambda energy of n photons: E = nhf = nhc/lambda algebraic solution: n = ..... substitute numbers ...... use calculator .... check units: dimensionless (correct)
Is the average force mentioned? In problem #2 one needs the correct definitions to solve it. One can not just take F = p/t (since that is totaly wrong), that is confusing (as you saw how the OP tried to solved it), using the correct defintions is the safest. As you said: "list all formulas"... And aslo: why converting everything to SI units? that is not an a priori thing to do... We solved this problem later in the PF chat me and _mayday_