How to Approach Questions Related to Waves

[_Mayday_]

Hey, I'm having a few problems with the questions below, now I think a lot of it is to do with not knowing how to approach the question. Please forgive me if there is not a lot 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_

 

[malawi_glenn]

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

 

[_Mayday_]

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.

 

[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:
$$E_{\gamma} = hf = hc/\lambda$$
?

 

[_Mayday_]

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.

 

[malawi_glenn]

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?

 

[_Mayday_]

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.

 

[malawi_glenn]

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).

 

[_Mayday_]

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 [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.

$$\frac{1.65\times10^{-18}{3\times10^8} = 5.52\times10^{-27}$$

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

 

[_Mayday_]

I can find the momentum as I have both E and c, so I can do E/c

 

[_Mayday_]

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...

 

[malawi_glenn]

no

force = time derivative of momentum

You can't GATHER force, force is instanteous.

So if the bulb casts away 20W photons in the same direction (we was to assue it was a parallel 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

 

[malawi_glenn]

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

 

[_Mayday_]

Malawi, I really have no idea at all!

 

[malawi_glenn]

Malawi, I really have no idea at all!

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?

 

[mikelepore]

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)

 

[malawi_glenn]

no energy is not = Power times t!

P = dE/dt, it is different from the AVERAGE Power: P = E/t

 

[mikelepore]

Is a time variation mentioned in the given problem?

 

[malawi_glenn]

Is a time variation mentioned in the given problem?

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_

 

[mikelepore]

My comments addressed only "Question 1" (constant power dissipation).

 

[malawi_glenn]

ok great