Find the radiator and radial lengths for a quarter-wave vertical or ground-plane antenna at any frequency.
A quarter-wave vertical needs a ground plane of radials or earth to work against. Radiator length in feet = 234 / frequency in MHz; the radials are cut about 5 percent longer. More radials, or longer ones over poor ground, improve efficiency.
The radiator in feet is 234 divided by the frequency in MHz, which is half a dipole leg. At 14.2 MHz that is about 16.5 feet (5.0 m). Radials are usually cut about 5 percent longer than the radiator.
Yes. A vertical works against a ground plane. Elevated verticals need at least two to four radials; ground-mounted ones benefit from many (16 to 32 or more) shallow radials, because they carry the return current and set the efficiency.
A vertical radiates at a low angle from a small footprint, which is good for DX and where there is no room or height for a dipole. The trade-off is more man-made noise pickup and a dependence on the ground system.