Atoms Test - 70...

The radius of the smaller electron orbit in hydrogen-like ion is $$\dfrac{0.51\times 10^{-10}}{4}$$m, then it is?

A single electron orbits around a stationary nucleus of charge $$+Ze$$, where $$Z$$ is a constant and $$e$$ is the magnitude of the electronic charge. It required $$47.2\ eV$$ to excite the electron from the second Bohr orbit to the third Bohr orbit.
Find the energy required to excite the electron from the third to the fourth Bohr orbit.

In an experiment on photoelectric effect photons of wavelength $$300\ nm$$ eject electrons from a metal of work function $$2.25\ eV$$. A photon of energy equal to that of the most energetic electron corresponds to the following transition in the hydrogen atom.

A diatomic molecules has moment of inertia $$I$$. By Bohr's quantization condition its rotational energy in the $$n^{th}$$ level $$(n = 0$$ is not allowed) is

A mixture of $$2$$ moles of helium gas (atomic mass $$=4$$ amu) and $$1$$ mole of argon gas (atomic mass $$=40$$ amu) is kept at $$300$$ K in a container. The ratio of the rms speeds $$\left(\dfrac{v_{rms}(helium)}{v_{rms}(argon)}\right)$$ is?

Which of the following statement is wrong?

A single electron orbits around a stationary nucleus of charge $$+Ze$$, where $$Z$$ is a constant and $$e$$ is the magnitude of the electronic charge. It required $$47.2\ eV$$ to excite the electron from the second Bohr orbit to the third Bohr orbit. Find the radius of the first Bohr orbit.
(The ionization energy of hydrogen atom $$13.6\ eV$$, Bohr radius $$= 5.3\times 10^{-11} m$$, speed of light $$= 3\times 10^{8} m/s$$, Planck's constant $$= 6.6\times 10^{-34} J-sec)$$.

In certain electronic transition from quantum level n to ground state in atomic hydrogen in one or more steps no line belonging to Brackett series is observed. The wave numbers which may be observed in Balmer series is then?

If velocity of $$\alpha  - $$particle is made $$1/3$$ times, then % variation in distance of closest approach will be: (with respect to initial)

In the Bohr's model of hydrogen-like atom the force between the nucleus and the electron is modified as
$$\quad F=\cfrac { { e }^{ 2 } }{ 4\pi { \varepsilon  }_{ 0 } } \left( \cfrac { 1 }{ { r }^{ 2 } } +\cfrac { \beta  }{ { r }^{ 3 } }  \right) $$, where $$\beta$$ is a constant. For this atom, the radius of the $$n$$th orbit in terms of the Bohr radius $$\left( { a }_{ 0 }=\cfrac { { \varepsilon  }_{ 0 }{ h }^{ 2 } }{ m\pi { e }^{ 2 } }  \right) $$ is: