[orgstudy]

I was given this question in my book …
A sphere of radius 1cm is placed in path of light of large aperture. The intensity of light is 0.5W/cm^2. The sphere completely absorbs photons falling on it. Find the force exerted by them on the sphere.
I solved the question and I have given the solution in the pic. Please have a look.

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Next there was another question given below it …
The same sphere is placed in same light but this time the sphere is not perfectly absorbing. Show that the force exerted by photons remains the same.

Well I have no idea how to prove the second one. Please someone help .

[Ari Ben Canaan]

This seems more Physics related.

I suggest you repost this same thread on this forum :http://www.physicsforums.com

[orgstudy]

This question is in my chemistry book ...
anyway i'll post it there. hope someone helps

[Grundalizer]

I still don't buy that photons have no mass.  How can something have momentum and no mass?

[orgstudy]

Well even i dont know how that happens.
I tried to find out but got no good explanation, so i gave up!!!!

[Borek]

I still don't buy that photons have no mass.  How can something have momentum and no mass?

You don't have to buy it, you have to accept it.

I don't understand it too, but then there are many things I don't understand, but I know they work - I assume this is one of these cases.

[orgstudy]

Ummmm ...

So you mean some heavenly voice said that "photons have momentum which can be found out using p=h/lambda ? and thats why we have to accept it without having any reason?

We are talking about science --- It says --- Everything has a REASON!!" ... weather you know it or not!!!

[Borek]

I have never told there is no reason. I don't know what the reason is, but I accept it works this way. Enough people that understand the subject much better then I do told me it is that way. I have never spent enough time and effort on studying the problem, so I have to rely on what others have already checked and proved. We do it all the time - you don't check every law you use studying first principles, quite often you just accept them as told.

Do you accept fact that Fermat's Last Theorem has been proved? I do. Do I understand the proof? No. But it has been checked by others.

[otivaeey]

I still don't buy that photons have no mass.  How can something have momentum and no mass?

In 1934, Tolman also defined relativistic mass as
m = E/c^2
which holds for all particles, including those moving at the speed of light.

Photon has no intrinsic mass/rest mass, but has relativistic mass/kinetic mass. The reason why photon is massless is still theoretical. Doubt it first, think forever.

[Juan R.]

For a perfect absorber

P_i = W S / c

where S is the surface and

P_f = 0

giving

| :delta: P | = | P_f - P_i | = W S / c

If the sphere is not a perfect absorber, call A the fraction of the initial light that is absorbed and B what is not. Then by conservation of energy

W = A + B

This means that

P_i = A S / c

and

P_f = - B S / c

Then

| :delta: P | = | P_f - P_i | = (A + B) S / c

| :delta: P | =  W S / c

What I do not understand is why you take S = pi r² instead of S= 2 pi r².

[Juan R.]

I still don't buy that photons have no mass.  How can something have momentum and no mass?

Because for a photon p is not mv, therefore a photon can have momentum without (rest) mass.

The general formula for free particles is

v = p c² / E     {1}

For a massive particle at low velocity, its energy can be approximated by E = m c² and {1} reduces to

v = p / m

that is the well-known non-relativistic expression

p = m v     {2}

For a massless particle moving at the speed of light, this expression {2} is not valid. In fact, {2} is not valid for a massive particle at high velocity (e.g., a relativistic electron), when the particle is not free (e.g., an electron in a magnetic field) or both.

For a massless particle its energy is E = pc and {1} reduces to

v = c

that is, massless particles always move at the speed of light. You did know this experimentally, now you understand why. Using this value for the v back into {1} gives us the momentum for massless particles

p = E / c     {3}