Consider an electron moving in the first Bohr orbit of a $$\mathrm{He}^{+}$$ ion with a velocity $$v_1$$. If it is allowed to move in the third Bohr orbit with a velocity $$v_3$$, then indicate the correct $$v_3: v_1$$ ratio.

Which hydrogen like species will have the same radius as that of $$1^{\text {st }}$$ Bohr orbit of hydrogen atom?

Two base balls (masses : m$$_1$$ = 100 g, and m$$_2$$ = 50 g) are thrown. Both of them move with uniform velocity, but the velocity of m$$_2$$ is 1.5 times that of m$$_1$$. The ratio of de Broglie wavelengths $$\lambda$$(m$$_1$$) : $$\lambda$$(m$$_2$$) is given by

The number of unpaired electron in Mn²⁺ ion is