A uniform magnetic field B exists in the region between $$x=0$$ and $$x=\frac{3R}{2}$$ (region 2 in the figure) pointing normally into the plane of the paper. A particle with charge $$+Q$$ and momentum $$p$$ directed along x-axis enters region 2 from region 1 at point $$P_{1}(Y=-R)$$.Which of the following option(s) is/are correct?

For $$B>\frac{2}{3}\frac{P}{QR}$$, the particle will re-enter region 1

For $$B=\frac{8}{13}\frac{P}{QR}$$, the particle will enter region 3 through the point $$P_{2}$$ on x-axis

When the particle re-enters region 1 through the longest possible path in region 2,the magnitude of the change in its linear momentum between point $$P_{1}$$ and the farthest point from axis is $$\frac{P}{\sqrt{2}}$$

For a fixed B, particles of same charge Q and same velocity V, the distance between the point $$P_{1}$$ and the point of re-entry into region 1 is inversely proportional to the mass of the particle