Why A quarter-wave vertical is the standard mobile/handheld whip because it works against a ground plane (the vehicle roof or radio chassis) to act like half of a dipole. The quarter-wave length in feet is roughly 234 divided by the frequency in MHz, so at about 146 MHz that is 234/146 = 1.6 feet, or roughly 19 inches. At resonance the antenna presents a near-resistive, low feedpoint impedance that matches 50-ohm coax well.
Watch out A resonant half-wave on 2 meters would be about twice as long, roughly 38 inches; a 19-inch whip is half of that. And a simple quarter-wave whip has essentially no gain over a dipole.
Quarter-wave feet = 234/f(MHz). 234/146 = 1.6 ft = 19 inches. Half-wave would be 38.
Two meters is about 78 inches; a quarter of 78 is about 19. So 19 inches is the quarter-wave, and a half-wave would be 38.