In ethene, there exists one sigma bond and one pi bond between the two carbon atoms.

Ethene, commonly referred to as ethylene, is a hydrocarbon with the chemical formula $C_2H_4$. It is the simplest alkene, characterized by the presence of a carbon-carbon double bond. This double bond consists of one sigma ($\sigma$) bond and one pi ($\pi$) bond.

The sigma bond is formed through the end-to-end or head-on overlap of two $\text{sp}^{2}$ hybrid orbitals, one contributed by each carbon atom. This overlap results in a region of high electron density between the two carbon atoms, leading to a strong sigma bond. Sigma bonds allow for free rotation because the overlapping orbitals maintain their degree of overlap, irrespective of any rotation around the bond axis.

In contrast, the pi bond arises from the sideways overlap of two unhybridized 2p orbitals, again one from each carbon atom. This overlap produces two regions of electron density, situated above and below the molecular plane. Unlike sigma bonds, pi bonds do not permit free rotation because any rotation would disrupt the parallel arrangement of the 2p orbitals, thus breaking the pi bond. For further insights into the molecular structure of alkenes like ethene, refer to additional resources.

The presence of the pi bond in ethene contributes to the molecule’s planar geometry, characterized by bond angles of approximately $120^\circ$. This planar structure results from the electron repulsion among the three $\text{sp}^{2}$ hybrid orbitals of each carbon atom, which strive to position themselves as far apart as possible. Additionally, the pi bond plays a significant role in the reactivity of ethene, as the electron-rich regions above and below the molecular plane are readily accessible to electrophiles. More information about the role of pi bonds can be found in related literature.

In summary, ethene features a sigma bond and a pi bond between its two carbon atoms. The sigma bond arises from direct orbital overlap, allowing for rotational freedom, while the pi bond is a result of the sideways overlap of p orbitals, which restricts rotation. This unique bonding configuration renders ethene a flat and reactive molecule, with its pi bond attracting substances that seek to react, thus imparting ethene with its distinct properties.