If c is the velocity of light in free space, the correct statements about photon among the following are:

A. The energy of a photon is E = hv.

B. The velocity of a photon is c.

C. The momentum of a photon, $p=\frac{hv}{c}$.

D. In a photon-electron collision, both total energy and total momentum are conserved.

E. Photon possesses positive charge.

Choose the correct answer from the options given below:

To identify the correct statements about a photon, let us analyze each statement step-by-step:

Statement A: The energy of a photon is $E=h\nu$.
According to Planck's quantum theory, electromagnetic radiation is emitted or absorbed in discrete packets of energy called photons or quanta. The energy of each photon is directly proportional to its frequency ($\nu$).
This is expressed as:
$E=h\nu$
where $h$ is Planck's constant. Thus, Statement A is correct.

Statement B: The velocity of a photon is c.
In free space (vacuum), all photons travel at the speed of light, which is denoted by $c$ (approximately $3\times {10}^8\text{m/s}$). This speed is independent of the frame of reference or the frequency of the photon. Thus, Statement B is correct.

Statement C: The momentum of a photon, $p=\frac{h\nu }{c}$.
From de Broglie's relation, the momentum ($p$) of a photon is related to its wavelength ($\lambda$) by:
$p=\frac{h}{\lambda }$
Since the velocity of light is related to frequency and wavelength by $c=\nu \lambda$, we can substitute $\lambda =\frac{c}{\nu }$ into the momentum equation:
$p=\frac{h\nu }{c}$
Alternatively, using Einstein's mass-energy equivalence, the energy is $E=pc$, which gives $p=\frac{E}{c}=\frac{h\nu }{c}$. Thus, Statement C is correct.

Statement D: In a photon-electron collision, both total energy and total momentum are conserved.
During collisions between photons and particles (such as an electron in the Compton effect or photoelectric effect), the collision is treated as an elastic collision. In any elastic collision, both the total energy and the total momentum of the system are conserved. However, the number of photons may not be conserved as a photon can be absorbed or a new photon can be created. Thus, Statement D is correct.

Statement E: Photon possesses positive charge.
Photons are electrically neutral particles. They do not carry any charge (neither positive nor negative) and are not deflected by electric or magnetic fields. Thus, Statement E is incorrect.

Comparing these findings, statements A, B, C, and D are correct.
Therefore, the correct option is A, B, C and D only.