Discussion
The intrinsic/permanent electric dipole moment in the ground state of hydrogen atom is (\(a_{0}\) is the Bohr radius)
Answer: B
The permanent electric dipole moment of the hydrogen ground state is zero.
The ground state, 1s, is spherically symmetric and has definite (even) parity. The dipole moment is the expectation value of \(-e\vec{r}\), and \(\vec{r}\) is odd under parity, so
\[ \begin{aligned} \langle \vec{d} \rangle &= -e\int |\psi_{100}|^{2}\,\vec{r}\,d^{3}r \\ &= 0 \end{aligned} \]
because the integrand is odd. The electron cloud is centred on the proton.
Values such as \(3ea_{0}\) appear in the linear Stark effect of the degenerate \(n = 2\) level, where states of opposite parity mix and the atom behaves as if it had a permanent dipole of that size. They do not apply to the non-degenerate ground state, which only acquires an induced dipole (the quadratic Stark effect).
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