Question 1 :
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 2 :
If elements of quantum number greater than $'n'$ were not allowed, the number of possible elements in nature would have been

Question 3 :
Check the correctness of the following statements about the Bohr Model of hydrogen atom:<br>$(i)$ The acceleration of the electron in $n=2$ orbit is more than that in $n=1$ orbit.<br>$(ii)$ The angular momentum of the electron in $n=2$ orbit is more than that in $n=1$ orbit.<br>$(iii)$ The KE of the electron in $n=2$ orbit is less than that in $n=1$ orbit

Question 4 :
<div>For $H$-like atoms :</div><div>&#160; &#160; &#160;&#160;</div><div>&#160; &#160; &#160; &#160; &#160; &#160; $\displaystyle E_n=-\frac{Z^2Rh}{n^2};u_n=\frac{u_1Z}{n}$ and $r_n=\frac{r_1\times n^2}{Z};$ where $Rh$ is Rydberg.<br/></div><br/>What is the potential energy of electron in $2^{nd}$ orbit of $H$-atom?<br/>

Question 5 :
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 6 :
The ratio of speed of electron in $I$ orbit of $H$-atom to $IV$ orbit of $He^+$ ion is :<br/>

Question 7 :
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 8 :
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 9 :
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 10 :
The number of revolutions of an electron in the second Bohr orbit in one second is:<br>

Question 11 :
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 12 :
Calculate the ratio of energies of $2^{nd}$ orbits of hydrogen, $He^+, Li^{+2}$.<br/>

Question 13 :
The quantum number n of the state finally populated in $He^{+}$ ions is&#160;<br/>

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 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 17 :
What is the energy required to move the electron from the ground state of H atom to the first excited state? Given that the ground state energy of H atom is 13.6 eV and that the energy E$_n$ of an electron in n$^{th}$ orbital of an atom or ion of atomic number Z is, given by the equation $E_n =(13.6Z^2/n^2)$

Question 18 :
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 19 :
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 20 :
The energy difference (in eV) between fourth and second orbits for $H$ atom is&#160;:

Question 21 :
The total energy of a hydrogen atom in its ground state is $-13.6\ eV$. If the potential energy in the first excited state is taken as zero then the total energy in the ground state will be:

Question 22 :
The ratio of ground state energy of $Li^{2+},&#160;He^+$ and H is :

Question 23 :
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 24 :
If the PE of a Bohr's hydrogen atom in the ground state is zero, then its total energy in the first excited state will be :

Question 25 :
Number of waves made by the pion when orbiting in third excitation state are

Question 26 :
The wavelength($\lambda_n$) of the pion orbiting in nth stationary state is given by