In Rutherford's experiment, number of particles scattered at $90^{\circ}$ angle are $x$ per second. Number particles scattered per second at angle $60^{\circ}$ is

When an $\alpha -$particle of mass $m$ moving with velocity $v$ bombards on a heavy nucleus of charge $Z_e$ , its distance of closest approach from the nucleus depends on $m$ as

In the Rutherford's nuclear model of the atom, the nucleus (radius about $10^{-15} \;m$ ) is analogous to the sun about which the electron move in orbit (radius $\approx 10^{-10} \;m$ ) like the earth orbits around the sun. If the dimensions of the solar system had the same proportions as those of the atom, would the earth be closer to or farther away from the sun than actually it is? The radius of earth's orbit is about $1.5 \times 10^{11} \;m.$ The radius of sun is taken as $7 \times 10^{8}\;m$

The binding energy of the electron in a hydrogen atom is $13.6\, eV$, the energy required to remove the electron from the first excited state of $Li^{++}$ is ......... $eV$

In the spectrum of hydrogen atom, the ratio of the longest wavelength in Lyman series to thelongest wavelength in the Balmer series is

The first line in the Lyman series has wavelength $\lambda $. The wavlength of the first line in Balmer series is