Question 1 :
The energy of the electron in the second and third Bohr orbits of the hydrogen atom is -5.42 $\times$ 10$^{-12}$ erg and -2.41 $\times$ 10$^{-12}$ erg, respectively. The wave length of the emitted radiation when the electron drops from third to second orbit will be :

Question 2 :
The angular speed $(\omega)$ of an electron revolving in $n^{th}$ Bohr orbit and corresponding principal quantum number(n) are related as ____________.

Question 3 :
The maximum possible values of magnetic orbital quantum number ($m_{l})$ are

Question 4 :
According to de-Broglie wavelength for electron in an orbit of hydrogen atom is $10^{-9}\ m$. The principle quantum number for this electron is

Question 5 :
As an electron is brought from an infinite distance close of nucleus of the atom, the energy of electron:

Question 6 :
The possible subshells in $n = 3$ energy shell are :

Question 7 :
The energy of second orbit of hydrogen is equal to the energy of:

Question 8 :
Which one of the following does not contains electrons in $4s$ subshells?<br/>Given that : Atomic numbers: $Ti=22,V=23,Cr=24,Mn=25$

Question 9 :
The Bohr orbit radius for the hydrogen atom $(n = 1)$ is approximately $0.530 \mathring{A}$ The radius for the first excited state $(n = 2)$ will be:

Question 10 :
The velocity of electron in third excited state of $\displaystyle Be^{3+}$&#160;will be:

Question 11 :
Consider a hydrogen like atom whose energy in $\displaystyle { n }^{ th }$&#160;excited state is given by $\displaystyle { E }_{ n }=-\frac { 13.6 }{ { n }^{ 2 } } { Z }^{ 2 }$. When this excited atom makes a transition from an excited state to ground state. The most energetic photons have energy $\displaystyle&#160;{ E }_{ max }=52.224eV$&#160;and the least energetic photons have energy&#160;$\displaystyle&#160;{ E }_{ min }=1.224eV$. Find the atomic number of atom.<br/>

Question 12 :
If the wavelength of the photon emitted from an electron jump n $=$ 4 to n $=$ 2 in a H-like species is 1216 $\overset{o}{A}$, then the species is :

Question 13 :
The only electron in the hydrogen atom resides under ordinary conditions on the first orbit. When energy is supplied, the electron moves to higher energy orbit depending on the amount of energy absorbed. When this electron returns to any of the lower orbits, it emits energy. Lyman series is formed when the electron returns the lowest orbit while Balmer series is formed when the electron returns to the second orbit. Similarly, Paschen, Brackett, and Pfind series are formed when electron returns to the third, fourth, and fifth from higher orbits, respectively.<br/>Maximum number of lines produced when an electron jumps from &#160;nth level to ground level is equal to $\displaystyle\frac{n(n - 1)}{2}$.&#160;<br/><i></i>If the electron comes back from the energy level having energy E$_2$ to the energy level having energy E$_1$, then difference may be expressed in terms of energy of photon as<br/>E$_2$ - E$_1$ = $\Delta$E, $\lambda$ = hc/$\Delta$E<br/>Since h and c are constant, $\Delta$E corresponds to definite energy, thus, each transition from one energy level to another will produce a light of definite wavelength. This is actually observed as a line in the spectrum of hydrogen atom.<br/>Wave number of line is given by the formula<br/>v = $RZ^2\left( \displaystyle\frac{1}{n_1^2} - \frac{1}{n_2^2}\right)$<br/>where R is a Rydberg constant.The wave number of electromagnetic radiation emitted during the transition of electron in between the two levels of Li$^{2+}$ ion whose principal quantum numbers sum is 4 and difference is 2 is :

Question 14 :
The longest wave length radiation emitted in the emission spectrum when the pion de-excites from n = 3 to ground state lies in which of the following region?

Question 15 :
Consider the hydrogen atom to be a proton embedded in a cavity of radius $a_0$ (Bohr's radius), whose charge is neutralized by the addition of an electron to the cavity in vacuum, infinitely slowly.&#160;Then the wavelength of the electron when it is at a distance of $a_0$ from the proton will be&#160;<br/>

Question 16 :
The ratio of ground state energy of $Li^{2+},&#160;He^+$ and H is :

Question 17 :
The ionization energy of hydrogen atom is $13.6$ eV.&#160;The longest wavelength of hydrogen spectrum in&#160;the ultraviolet region is expected to be:

Question 18 :
Electrons accelerated by potential V are diffracted from a crystal. If $\mathrm{d}= 1\mathrm{A}$ and $\mathrm{i}=30^{0},\ \mathrm{V}$ should be about:&#160;<div>[$\mathrm{h}=6.6\times 10^{-34}$ Js, $\mathrm{m}_{\mathrm{e}}=9.1\times 10^{-31}$ kg, $\mathrm{e}=1.6\times 10^{-19}\mathrm{C}$]<br/></div>

Question 19 :
The number of revolutions of an electron in the second Bohr orbit in one second is:<br>

Question 20 :
Calculate the ratio of energies of $2^{nd}$ orbits of hydrogen, $He^+, Li^{+2}$.<br/>