Which of the following statement(s) is(are) correct about the spectrum of the hydrogen atom?

A long straight wire carries a current, I = 2 ampere. A semi-circular conducting rod is placed beside it on two conducting parallel rails of negligible resistance. Both the rails are parallel to the wire. The wire, the rod and the rails lie in the same horizontal plane, as shown in the figure. Two ends of the semi-circular rod are at the distances 1 cm and 4 cm from the wire. At time t = 0, the rod starts moving on the rails with a speed v = 3.0 m/s (see the figure).

A resistor R = 1.4 $$\Omega$$ and a capacitor C₀ = 5.0$$\mu$$F are connected in series between the rails. At time t = 0, C₀ is uncharged. Which of the following statement(s) is(are) correct? [$$\mu$$₀ = 4$$\pi$$ $$\times$$ 10^$$-$$7 SI units. Take ln 2 = 0.7]

A cylindrical tube, with its base as shown in the figure, is filled with water. It is moving down with a constant acceleration a along a fixed inclined plane with angle $$\theta$$ = 45$$^\circ$$. P₁ and P₂ are pressures at points 1 and 2, respectively, located at the base of the tube. Let $$\beta$$ = (P₁ $$-$$ P₂)/($$\rho$$gd), where $$\rho$$ is density of water, d is the inner diameter of the tube and g is the acceleration due to gravity. Which of the following statement(s) is(are) correct?

An $$\alpha$$-particle (mass 4 amu) and a singly charged sulphur ion (mass 32 amu) are initially at rest. They are accelerated through a potential V and then allowed to pass into a region of uniform magnetic field which is normal to the velocities of the particles. Within this region, the $$\alpha$$-particle and the sulfur ion move in circular orbits of radii r_$$\alpha$$ and r_s, respectively. The ratio (r_s/r_$$\alpha$$) is __________.