We evaluate each statement one by one.

Option A: Photon has momentum as well as wavelength.

• For a photon, $p = \frac{h}{\lambda}$
• So a photon has both momentum and wavelength.
• Option A is true.

Option B: Splitting of spectral lines in electrical field is called Stark effect.

• Splitting in an electric field is indeed called the Stark effect.
• (For comparison, splitting in a magnetic field is the Zeeman effect.)
• Option B is true.

Option C: Rydberg constant has unit of energy.

• The Rydberg constant $R$ appears in $\bar{\nu} = R\left(\frac{1}{n_1^2} - \frac{1}{n_2^2}\right)$
• Here $\bar{\nu}$ is wave number, whose unit is $\text{length}^{-1}$, usually $\text{m}^{-1}$.
• Therefore, the unit of the Rydberg constant is also $\text{m}^{-1}$, not energy.
• Option C is false.

Option D: Frequency of emitted radiation from a black body goes from a lower wavelength to higher wavelength as the temperature increases.

• By Wien’s displacement law, $\lambda_{\max} T = \text{constant}$
• As temperature increases, $\lambda_{\max}$ decreases.
• That means the peak shifts from higher wavelength to lower wavelength, and hence frequency increases.
• So the wording in D is incorrect if interpreted literally.
• Option D is also false.

Since this is a single correct MCQ, we should identify the best false statement expected in atomic structure context.

• Option C is unambiguously false because the Rydberg constant definitely does not have units of energy.
• Option D seems to contain a phrasing issue mixing frequency and wavelength, but many exam keys may target Wien’s law. Still, as written, C is certainly false.

Derived answer: $\boxed{\text{C}}$