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When an electron makes a transition from (n+1) state to nth state, the frequency of emitted radiations is related to n according to (n>>1):
1. $\mathrm{v}=\frac{2{\mathrm{cRZ}}^2}{{\mathrm{n}}^3}$
2. $\mathrm{v}=\frac{{\mathrm{cRZ}}^2}{{\mathrm{n}}^4}$
3. $\mathrm{v}=\frac{{\mathrm{cRZ}}^2}{{\mathrm{n}}^2}$
4. $\mathrm{v}=\frac{2{\mathrm{cRZ}}^2}{{\mathrm{n}}^2}$

An electron is allowed to move freely in a closed cubic box of length of side 10 cm. The maximum uncertainty in its velocity will be :
1. $3.35\times {10}^{-3} \mathrm{m} {\sec }^{-1}$
2. $5.8\times {10}^{-4} \mathrm{m} {\sec }^{-1}$
3. $4\times {10}^{-5} \mathrm{m} {\sec }^{-1}$
4. $4\times {10}^{-6} \mathrm{m} {\sec }^{-1}$

An element undergoes a reaction as shown :
$\mathrm{X}+2{\mathrm{e}}^{-}\to {\mathrm{X}}^{2-}$, energy released = 30.87 eV/atom. If the energy released, is used to dissociate 4 gms of H₂ molecules, equally into ${\mathrm{H}}^{+ }\mathrm{and} {\mathrm{H}}^{*}$ where ${\mathrm{H}}^{*}$ is excited state of atoms where the electron travels in orbit whose circumference equal to four times its De-Broglie wavelength. Determine the least moles of X that would be required :
Given : I.E. of H = 13.6 eV/atom, bond energy of  H₂ = 4.526 eV/molecule
1. 1
2. 2
3. 3
4. 4 

If the energy of H-atom in the ground state is -E, the velocity of photo-electron emitted when a photon having enrgy E_p strikes a stationary Li²⁺ ion in ground state, is given by :
1. $\mathrm{v}=\sqrt{\frac{2\left({\mathrm{E}}_{\mathrm{p}}-\mathrm{E}\right)}{\mathrm{m}}}$
2. $\mathrm{v}=\sqrt{\frac{2\left({\mathrm{E}}_{\mathrm{p}}+9\mathrm{E}\right)}{\mathrm{m}}}$
3. $\mathrm{v}=\sqrt{\frac{2\left({\mathrm{E}}_{\mathrm{p}}-9\mathrm{E}\right)}{\mathrm{m}}}$
4. $\mathrm{v}=\sqrt{\frac{2\left({\mathrm{E}}_{\mathrm{p}}-3\mathrm{E}\right)}{\mathrm{m}}}$

At which temperature will the translational kinetic energy of H-atom equal to that for H-atom of first line Lyman transition ? (Given $\mathrm{N}=6\times {10}^{23}$)
1. 780 K
2. $1.32\times {10}^5 \mathrm{K}$
3. $7.84\times {10}^4 \mathrm{K}$
4. 1000 K

For a 3s-orbital
$\mathrm{\psi }\left(3\mathrm{s}\right)=\frac{1}{9\sqrt{3}}{\left(\frac{1}{{\mathrm{a}}_0}\right)}^{3/2}\left(6-6\mathrm{\sigma }+{\mathrm{\sigma }}^2\right){\mathrm{\sigma }}^{-\mathrm{\sigma }/2}; \mathrm{where} \mathrm{\sigma }=\frac{2\mathrm{r}.\mathrm{Z}}{3{\mathrm{a}}_0}$
What is the maximum radial distance of node from nucleus ?
1. $\frac{\left(3+\sqrt{3}\right){\mathrm{a}}_0}{\mathrm{Z}}$
2. $\frac{{\mathrm{a}}_0}{\mathrm{Z}}$
3. $\frac{3}{2}\frac{\left(3+\sqrt{3}\right){\mathrm{a}}_0}{\mathrm{Z}}$
4. $\frac{2{\mathrm{a}}_0}{\mathrm{Z}}$

Monochromatic radiation of specific wavelength is incident on H-atom in ground state. H-atom absorbs energy and emit subsequently radiations of six different wavelength. Find wavelength of incident radiations
1. 9.75 nm
2. 50 nm
3. 85.8 nm
4. 97.25 nm

If in Bohr's model, for unielectron atom, time period of revolution is represented as ${\mathrm{T}}_{\mathrm{n},\mathrm{Z}}$ where n represents shell no. and Z represents atomic number tham the value of ${\mathrm{T}}_{1,2}:{\mathrm{T}}_{2,1}$ will be 
1. 8:1
2. 1:8
3. 1:1
4. 1:32

What is the ratio of time periods $\left({\mathrm{T}}_1/{\mathrm{T}}_2\right)$ in second orbit of hydrogen atom to third orbit of ${\mathrm{H}}^{+}$ ion?
1. 8/27
2. 32/27
3. 27/32
4. None of these

${\mathrm{Be}}^{3+}$ion and a proton are accelerated by the same potential. The ratio of their de-Broglie wavelengths is
(assume mass of proton =  mass of neutron)
1. 1:2
2. 1:4
3. 1:1
4. 1:$3\sqrt{3}$

The mass of an electron is m, charge is e and it is accelerated from rest through a potential difference of V volts. The velocity acquired by electron will be :
1. $\sqrt{\frac{\mathrm{V}}{\mathrm{m}}}$
2. $\sqrt{\frac{\mathrm{eV}}{\mathrm{m}}}$
3. $\sqrt{\frac{2\mathrm{eV}}{\mathrm{m}}}$
4. zero

If the ionization energy of ${\mathrm{He}}^{+}$ is $19.6\times {10}^{-18} \mathrm{J}$ per atom then the energy of ${\mathrm{Be}}^{3+}$ ion in the second stationary state is :
1. $-4.9\times {10}^{-18} \mathrm{J}$
2. $-44.1\times {10}^{-18} \mathrm{J}$
3. $-11.025\times {10}^{-18} \mathrm{J}$
4. None of these

Find the value of wave number $\left(\overline{\mathrm{v}}\right)$ in terms of Rydberg's constant, when transition of electron takes place betweem two levels of ${\mathrm{He}}^{+}$ ion whose sum is 4 and difference is 2
1. $\frac{8\mathrm{R}}{9}$
2. $\frac{32\mathrm{R}}{9}$
3. $\frac{3\mathrm{R}}{4}$
4. None of these

An excited state of H atom emits a photon of wavelength $\mathrm{\lambda }$ and returns in the ground state, the prinicipal quantum number of excited state is given by:
1. $\sqrt{\mathrm{\lambda R}\left(\mathrm{\lambda R}-1\right)}$
2. $\sqrt{\frac{\mathrm{\lambda R}}{\left(\mathrm{\lambda R}-1\right)}}$
3. $\sqrt{\mathrm{\lambda R}\left(\mathrm{\lambda R}+1\right)}$
4. $\sqrt{\frac{\left(\mathrm{\lambda R}-1\right)}{\mathrm{\lambda R}}}$

A dye absorbs a photon of wavelength $\mathrm{\lambda }$ and re-emits the same energy into two photons of wavelengths ${\mathrm{\lambda }}_1$ and ${\mathrm{\lambda }}_2$ respectively. The wavelength $\mathrm{\lambda }$ is related ${\mathrm{\lambda }}_1$ and ${\mathrm{\lambda }}_2$ as :
1. $\mathrm{\lambda }=\frac{{\mathrm{\lambda }}_1+{\mathrm{\lambda }}_2}{{\mathrm{\lambda }}_1{\mathrm{\lambda }}_2}$
2. $\mathrm{\lambda }=\frac{{\mathrm{\lambda }}_1{\mathrm{\lambda }}_2}{{\mathrm{\lambda }}_1+{\mathrm{\lambda }}_2}$
3. $\mathrm{\lambda }=\frac{{\mathrm{\lambda }}_1^2{\mathrm{\lambda }}_2^2}{{\mathrm{\lambda }}_1+{\mathrm{\lambda }}_2}$
4. $\mathrm{\lambda }=\frac{{\mathrm{\lambda }}_1{\mathrm{\lambda }}_2}{{\left({\mathrm{\lambda }}_1+{\mathrm{\lambda }}_2\right)}^2}$

If ${\mathrm{a}}_0$ be the radius of first Bohr's orbit of H-atom, the de-Broglie's wavelength of an electron revolving in the second Bohr's orbit will be :
1. $6{\mathrm{\pi a}}_0$
2. $4{\mathrm{\pi a}}_0$
3. $2{\mathrm{\pi a}}_0$
4. None of these

Which electronic transition in a hydrogen atom, starting from the orbit n =7, will produce infrared light of wavelength of 2170 nm? (Given : ${\mathrm{R}}_{\mathrm{H}}=1.09677\times {10}^7 {\mathrm{m}}^{-1}$)
1. n=7 to n=6
2. n=7 to n=5
3. n=7 to n=4
4. n=7 to n=3

A hydrogen atom in the ground state is excited by monochromatic radiation of wavelength $\mathrm{\lambda } \stackrel{\mathrm{o}}{\mathrm{A}}$. The resulting spectrum consists of maximum 15 different lines. What is the wavelength $\mathrm{\lambda }$? $\left({\mathrm{R}}_{\mathrm{H}}=109737 {\mathrm{cm}}^{-1}\right)$
1. 937.3 $\stackrel{0}{\mathrm{A}}$
2. 1025 $\stackrel{0}{\mathrm{A}}$
3. 1236 $\stackrel{0}{\mathrm{A}}$
4. None of these

The Schrodinger wave equation for hydrogen atom is 
$\mathrm{\psi }\left(\mathrm{radial}\right)=\frac{1}{16\sqrt{4}}{\left(\frac{\mathrm{Z}}{{\mathrm{a}}_0}\right)}^{3/2}\left[\left(\mathrm{\sigma }-1\right)\left({\mathrm{\sigma }}^2-8\mathrm{\sigma }+12\right)\right]{\mathrm{e}}^{-\mathrm{\sigma }/2}$
where ${\mathrm{a}}_0$ and Z are the constant in which answer can be expressed and $\mathrm{\sigma }=\frac{27\mathrm{r}}{{\mathrm{a}}_0}$ minimum and maximum position of radial nodes from nucleus are ..... respectively.
1. $\frac{{\mathrm{a}}_0}{\mathrm{Z}},\frac{3a_0}{Z}$
2. $\frac{{\mathrm{a}}_0}{2\mathrm{Z}},\frac{a_0}{Z}$
3. $\frac{{\mathrm{a}}_0}{2\mathrm{Z}},\frac{\mathit{3}{a}_0}{Z}$
4. $\frac{{\mathrm{a}}_0}{2\mathrm{Z}},\frac{\mathit{4}{a}_0}{Z}$

If ${\mathrm{\lambda }}_0 \mathrm{and} \mathrm{\lambda }$ be the threshold wavelength and the wavelength of incident light, the velocity of photo-electrons ejected from the metal surface is :
1. $\sqrt{\frac{2\mathrm{h}}{\mathrm{m}}\left({\mathrm{\lambda }}_0-\mathrm{\lambda }\right)}$
2. $\sqrt{\frac{2\mathrm{hc}}{\mathrm{m}}\left({\mathrm{\lambda }}_0-\mathrm{\lambda }\right)}$
3. $\sqrt{\frac{2\mathrm{hc}}{\mathrm{m}}\left(\frac{{\mathrm{\lambda }}_0-\mathrm{\lambda }}{{\mathrm{\lambda }}_0\mathrm{\lambda }}\right)}$
4. $\sqrt{\frac{2\mathrm{h}}{\mathrm{m}}\left(\frac{1}{{\mathrm{\lambda }}_0}-\frac{1}{\mathrm{\lambda }}\right)}$

A light source of wavelength $\mathrm{\lambda }$ illuminates a metal and ejects photo-electrons with (K.E.)_max = 1eV
Another light source of wavelength $\frac{\mathrm{\lambda }}{3}$, ejects photo-electrons from same metal with (K.E.)_max = 4 eV .Find the value of work function?
1. 1eV
2. 2 eV
3. 0.5 eV
4. None of these