MCQ : Comparing characteristics of two photons

[Jahnavi]

Homework Statement

Homework Equations

The Attempt at a Solution

I am surely making some very silly mistake in this problem . Presuming linear momenta means magnitude of momentum , to me all four options look correct .

a) since wavelengths are same , energy is same which means momentum is same .option a) is correct .

Similarly b) , c) , d) are correct .

Or is it that the question is considering momentum as a vector (which it is ) but generally in these problems only magnitude of momentum is considered .

If this is the case , option d) is correct .

Please let me know which is correct .

 

[kuruman]

I think the question wants you to consider momentum as a vector. Compare (a) and (d). Only one of them can be correct.

 

[Jahnavi]

I think the question wants you to consider momentum as a vector. Compare (a) and (d). Only one of them can be correct.

I think d) will be correct .

 

[kuruman]

I agree.

 

[Jahnavi]

In the relation E = Pc for a photon, are both the terms on RHS (momentum and speed ) treated as vectors and is it that a dot product is taken so as to get the energy term E ?

 

[kuruman]

In the relation E = Pc for a photon, are both the terms on RHS (momentum and speed ) treated as vectors and is it that a dot product is taken so as to get the energy term E ?

$E=pc$ is a scalar equation containing scalars only. I cannot think of a situation in which the momentum and the velocity are in different directions. Can you?

 

[Jahnavi]

No

I asked because E = Pc doesn't involve vectors whereas in the OP direction of momentum vector was to be considered while relating to wavelength (energy ) .

 

[kuruman]

No
I asked because E = Pc doesn't involve vectors whereas in the OP direction of momentum vector was to be considered while relating to wavelength (energy ) .

Yes, but as you have gathered already by now only (d) is necessarily correct. However, all four answers would be correct if the two photons travel in the same direction. The way one answers this question depends on one's assumptions. In my opinion it's not a well-crafted question because it leaves room for ambiguity. A well-crafted $N$ choice question should have one necessarily correct answer and $N-1$ choices that cannot possibly be correct.

 

[Jahnavi]

Thanks !