Bohr's model describes hydrogen-like atoms with quantized orbits. The energy of an orbit is given by $E=-\frac{Z{}^{2}R}{n^2}$, where Z is atomic number, R is Rydberg constant, and n is the principal quantum number.

The distance between orbits increases with n, so the first statement is incorrect. The energy difference between successive levels decreases as n increases, so the third statement is correct. For He⁺ (Z=2), ground state energy is -4R = -54.4eV. A 30eV photon cannot excite it (needs at least 40.8eV), so the second statement is incorrect. For Li²⁺ (Z=3), ionization energy is 9R, so the fourth statement is correct.

Final Answer: The first and second statements are incorrect.