Question 1 :
The two electrons have the following sets of quantum numbers.<br/>X: 3, 2, -2, +1/2<br/>Y: 3, 0, 0, + 1/2<br/>What is true of the following?

Question 2 :
Which of the following parameters are same for all hydrogen like atoms and ions in their ground state?

Question 4 :
According to the Bohr model of the atom, which electron transition will emit the lowest energy photon?

Question 5 :
The first ionization energy of $N$ &amp; $O$ are __________ respectively .

Question 6 :
Calculate the number of revolutions/sec around the nucleus of an electron placed in III orbit of $H$-atom.<br/>

Question 7 :
Calculate the radius of Bohr's first orbit for hydrogen atom and the energy of electron in this orbit:

Question 8 :
If the radius of second stationary orbit (in Bohr's atom) is R. Then, the radius of third orbit will be:

Question 9 :
<div>State True or False.<br/></div>A negative energy state is more stable relative to a zero energy state.<br/>

Question 10 :
For any H like system, the ratio of velocities of orbit I, II &amp; III&#160; i.e.&#160;$\displaystyle V_{1}: V_{2}: V_{3}$ will be :

Question 11 :
Assertion: 3s, 3p and 3d subshells of hydrogen have the same energy. <br/>Reason: Energy of subshells in the hydrogen atom, depends on the principal quantum number (n) and azimuthal quantum number (l).&#160;<br/>

Question 13 :
A particle of mass $m$ moves around in a circular&#160;orbit in a centro symmetric potential field u(r)$=\dfrac{kr^{2}}{2}$. Using Bohr&#8217;s quantization rule, the permissible&#160;energy levels are&#160;<br/>

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 :
If elements of quantum number greater than $'n'$ were not allowed, the number of possible elements in nature would have been

Question 16 :
The energy of the second Bohr orbit in the hydrogen atom is $-3.41 \,eV.$ The energy of the second Bohr orbit of $He^{+}$ ion would be:

Question 17 :
The quantum number n of the state finally populated in $He^{+}$ ions is&#160;<br/>

Question 18 :
A hydrogen-like atom (atomic number $Z$) is in a higher excited state of the quantum number $n$. This excited atom can make a transition to the first excited state by successfully emitted to photons of energies $10.20eV$ and $17.00eV$ respectively.<div>&#160; &#160; &#160; &#160;Alternatively, the atom from the same excited state can make a transition to the second excites state by the successively emitting two photons of energy $4.25ev$ and $5.95ev$ respectively. Determine the values of $n$ and $Z$ (ionization energy of hydrogen atom $=13.6eV$).<br/></div>

Question 19 :
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 20 :
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>