Given below are two statements:
Statement I: Two photons having equal linear momenta have equal wavelengths.
Statement II: If the wavelength of the photon is decreased, then the momentum and energy of a photon will also decrease.
In the light of the above statements, choose the correct answer from the options given below.

We analyse each statement one by one.

Statement I: The momentum of a photon is given by $$p = \frac{h}{\lambda}$$, where $$h$$ is Planck's constant and $$\lambda$$ is the wavelength. If two photons have equal linear momenta, then $$\frac{h}{\lambda_1} = \frac{h}{\lambda_2}$$, which gives $$\lambda_1 = \lambda_2$$. So two photons with equal linear momenta must have equal wavelengths. Statement I is true.

Statement II: The momentum of a photon is $$p = \frac{h}{\lambda}$$ and its energy is $$E = \frac{hc}{\lambda}$$. If the wavelength $$\lambda$$ decreases, then $$p = \frac{h}{\lambda}$$ increases (since $$\lambda$$ is in the denominator). Similarly, $$E = \frac{hc}{\lambda}$$ also increases. So when wavelength decreases, both momentum and energy increase, not decrease. Statement II is false.

Hence, the correct answer is Option C.