Given below are two statements:
Statement I : Hyperconjugation is a permanent effect.
Statement II : Hyperconjugation in ethyl cation $$\left(CH_3 - \overset{+}{CH_2}\right)$$ involves the overlapping of $$C_{sp^2} - H_{1s}$$ bond with empty 2p orbital of other carbon.
Choose the correct option:

We begin by recalling that in any organic molecule there are two broad kinds of electronic effects - permanent effects, which are present in the molecule in the ground state itself, and temporary or induced effects, which appear only in the presence of an external reagent or field. The hyperconjugation effect belongs to the first category because the delocalisation of electrons arising from it is built into the normal electronic structure of the molecule; no attacking reagent is required to set it up. Therefore hyperconjugation is indeed a permanent effect.

Hence, Statement I, “Hyperconjugation is a permanent effect”, is correct.

Now let us examine the mechanistic picture of hyperconjugation in the ethyl cation $$CH_3-CH_2^+.$$ The second carbon (the positively charged one) is $$sp^2$$-hybridised, so three of its $$sp^2$$ orbitals form $$\sigma$$-bonds with two hydrogens and with the adjacent carbon, while the remaining unhybridised orbital is a vacant $$2p$$ orbital perpendicular to the molecular plane.

The electrons that can be donated through hyperconjugation are the $$\sigma$$ electrons of the C-H bonds on the neighbouring $$\beta$$-carbon, i.e. the $$CH_3$$ group. Each such bond is built from

filled }C_{sp^3}\;( $$\text{on the }$$CH_3$$\text{ carbon}$$) \;+\;$$\text{filled }$$H_{1s

Expressed symbolically, one of these bonds can be written as

$$\sigma\bigl(C_{sp^3}-H_{1s}\bigr).$$

For hyperconjugation to operate, only the carbon lobe (the $$C_{sp^3}$$ part) of this bond can align laterally with the empty $$2p$$ orbital on the positively charged carbon; the spherical $$1s$$ orbital on hydrogen has no directional preference and therefore cannot overlap sideways with that $$2p$$ orbital. In other words, the interaction is effectively between

$$\boxed{\text{filled } C_{sp^3} \text{ lobe}}$$ and $$\boxed{\text{empty } 2p \text{ orbital on } C^+}.$$

The statement given in the question reads: “Hyperconjugation in ethyl cation involves the overlapping of $$C_{sp^3}-H_{1s}$$ bond with empty $$2p$$ orbital of other carbon.” Because it speaks of the entire $$C_{sp^3}-H_{1s}$$ bond overlapping with the vacant $$2p$$ orbital, it implicitly involves the hydrogen end as well, which is not capable of the required sideways overlap. Strictly, only the carbon end of the bond participates. Thus the wording of Statement II is inaccurate, and the statement is taken as false.

We therefore have: Statement I true, Statement II false.

Hence, the correct answer is Option C.