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If you have 2 hydrogen atoms and in which electrons are present at 4th level and these electrons jumps to ground level. How many maximum spectral lines are obtained?
1. 6
2. 5
3. 4
4. 3

 The relationship between the energy \(E_1\) of radiation with a wavelength of \(8000\) Å and the energy \(E_2\)​ of radiation with a wavelength of \(1600\) Å is:
1. \(E_1=2E_2\)
2. \(E_1=4E_2\)
3. \(E_1=6E_2\)
4. \(E_1=E_2\)${\mathrm{}}_{}$

The ratio of the radii of the first three Bohr orbit in H atom is
1. $1:\frac{1}{2}:\frac{1}{3}$
2. $1 : 2 : 3$
3. 1 : 4: 9
4. 1 : 8 : 27

In an atom two electrons move around the nucleus in circular orbits of radii R and 4R. The ratio of the time taken by them to complete one revolution is :
1. 1 : 4
2. 4 : 1
3. 1 : 8
4. 8 : 7

$\mathrm{The} \mathrm{orbital} \mathrm{configuration} \mathrm{of}{ }_{24}\mathrm{Cr} \mathrm{is} 3{\mathrm{d}}^5 4{\mathrm{s}}^1 . \mathrm{The} \mathrm{number} \mathrm{of} \mathrm{unpaired} \mathrm{electrons} \mathrm{in} {\mathrm{Cr}}^{3+}$
1. 3
2. 2
3. 1
4. 4

$$\begin{gathered} \mathrm{Which} \mathrm{of} \mathrm{the} \mathrm{following} \mathrm{is} \mathrm{the} \mathrm{correct} \mathrm{set} \mathrm{of} \mathrm{quantum} \mathrm{numbers} \mathrm{for} \mathrm{the} \\ \mathrm{outer} \mathrm{shell} \mathrm{electrons} \mathrm{of}{ }_{21}\mathrm{Sc} ? \end{gathered}$$
1. 3, 2, 0,+ 1/2
2. 4, 0, 0,+1/2
3. 3, 0, 0,–1/2
4. 4, 0, –1,+1/2

The electronic configuration of a dipositive ion M2+ is 2, 8, 14 and its mass number is 56. The number of neutrons present in
1. 32
2. 42
3. 30
4. 34

The kinetic energy of the photoelectrons does not depend upon
1. Intensity of incident radiation
2. Frequency of incident radiation
3. Wavelength of incident radiation
4. Wave number of incident radiation

The work function of a metal is 4.2 eV. If radiations of 2000 Å fall on the metal then the kinetic energy of the fastest photo electron is
$1. 1.6 \times 10{–}^{19} \mathrm{J}$
$2. 16 \times {10}^{10} \mathrm{J}$
$3. 3.2 \times 10{–}^{19} \mathrm{J}$
$4. 6.4 \times 10{–}^{10} \mathrm{J}$
 

According to Bohr’s theory the angular momentum of an electron in the fourth orbit is
1. $\frac{h}{2\mathrm{\pi }}$
2. $\frac{2h}{\mathrm{\pi }}$
3. $\frac{3h}{2\mathrm{\pi }}$
4. $\frac{3h}{\mathrm{\pi }}$

The transition of electrons in H atom that will emit maximum energy is :
$1. {\mathrm{n}}_{3 }\to {\mathrm{n}}_2$
$2. n_4\to n_3$
$3. n_5\to n_4$
$4. n_6\to n_5$

$\mathrm{For} \mathrm{the} \mathrm{electronic} \mathrm{transition} \mathrm{from} \mathrm{n} = 2\to \mathrm{n} =1 \mathrm{which} \mathrm{of} \mathrm{the} \mathrm{following} \mathrm{will} \mathrm{produce} \mathrm{shortest} \mathrm{wavelength} ?$
1. H atom
2. D atom
$3. {\mathrm{He}}^{+} \mathrm{ion}$
$4. {\mathrm{Li}}^{2+} \mathrm{ion}$

In Bohr’s model of the hydrogen atom the ratio between the period of revolution of an electron in the orbit n = 1 to the period of revolution of the electron in the orbit n = 2 is
1. 1 : 2
2. 2 : 1
3. 1 : 4
4. 1 : 8

$\mathrm{A} \mathrm{cricket} \mathrm{ball} \mathrm{of} 0.5 \mathrm{kg} \mathrm{is} \mathrm{moving} \mathrm{with} \mathrm{a} \mathrm{velocity} \mathrm{of} 100 {\mathrm{ms}}^{-1}. \mathrm{The} \mathrm{wavelength} \mathrm{associated} \mathrm{with} \mathrm{its} \mathrm{motion} \mathrm{is} :$
1. 1/100 cm
$2. 6.6 \times {10}^{-34} \mathrm{m}$
$3. 1.32 \times {10}^{-35} \mathrm{m}$
$4. 6.6 \times {10}^{-28}\mathrm{m}$

If uncertainties in the measurement of position and momentum are equal, the uncertainty in the measurement of velocity is:
1. $\frac{1}{2}\sqrt{\frac{\mathrm{mh}}{\mathrm{\pi }}}$
$2. \frac{1}{2\mathrm{\pi }}\sqrt{\frac{\mathrm{h}}{\mathrm{m}}}$
$3. \frac{1}{2\mathrm{m}}\sqrt{\frac{\mathrm{h}}{\mathrm{\pi }}}$
4. None of these

The total number of electrons in a subshell designated by azimuthal quantum number, l is given as
1. 2$l$ + 1
$2. l^{\mathit{2}}$
$3. 4l + 2$
$4. 2l + 2$

$\mathrm{How} \mathrm{many} \mathrm{electrons} \mathrm{in}{ }_{19}\mathrm{K} \mathrm{have} \mathrm{n} = 3; l = 0?$
1. 1
2. 2
3. 4
4. 3

Which of the following sets of quantum numbers is impossible arrangement ?
1. n = 3, m = –2, s=+1/2
2. n = 4, m = +3, s = +1/2
3. n = 5, m = +2, s=–1/2
4. n = 3, m = –3, s = –1/2

For d-electron, the orbital angular momentum is
$1. \sqrt{6}\frac{\mathrm{h}}{2\mathrm{\pi }}$
2. $\sqrt{2}\frac{\mathrm{h}}{2\mathrm{\pi }}$
3. $\mathrm{h}/2\mathrm{\pi }$
4. $2\mathrm{h}/\mathrm{\pi }$

Calculate the spectral lines that are obtained in the visible region when an electron jumps from n=5 to n=1 hydrogen atom.
1. 3
2. 4
3. 6
4. 10

A single electron in an ion has ionization energy equals to 217.6 eV. What is the total number of neutrons present in one ion of it?
1. 2
2. 4
3. 5
4. 9

The ratio of the radius diffrerence between $4^{\mathrm{th}}$ and $3^{\mathrm{rd}}$ orbit of H-atom and that of ${\mathrm{Li}}^{2+}$ ion is :
1. 1:1
2. 3:1
3. 3:4
4. 9:1

$\mathrm{The} \mathrm{velocity} \mathrm{of} \mathrm{an} \mathrm{electronin} \mathrm{excited} \mathrm{state} \mathrm{of} \mathrm{H}-\mathrm{atom} \mathrm{is} 1.093\times {10}^6 \mathrm{m}/\mathrm{s}. \mathrm{What} \mathrm{is} \mathrm{the} \mathrm{circumference} \mathrm{of} \mathrm{this} \mathrm{orbit}?$
$$\begin{gathered} 1. 3.32\times {{10}^{-10}}^{}{\mathrm{m}}^{} \\ 2. 6.64\times {10}^{-10}\mathrm{m} \\ 3. 13.30\times {10}^{-10}\mathrm{m} \\ 4. 13.28\times {10}^{-8}\mathrm{m} \end{gathered}$$

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

$$\begin{gathered} \mathrm{An} \mathrm{elecment} \mathrm{undergoes} \mathrm{a} \mathrm{reaction} \mathrm{as} \mathrm{shown} : \\ \mathrm{X} + 2{\mathrm{e}}^{-}\to {\mathrm{X}}^{2-}, \mathrm{energy} \mathrm{released} = 30.87 \mathrm{eV}/\mathrm{atom}. \\ \mathrm{if} \mathrm{the} \mathrm{energy} \mathrm{released}, \mathrm{is} \mathrm{used} \mathrm{to} \mathrm{dissociat} 4 \mathrm{gms} \mathrm{of} {\mathrm{H}}_{2 }\mathrm{molecules}, \\ \mathrm{equally} \mathrm{into} {\mathrm{H}}^{+} \mathrm{and} \mathrm{H}*, \mathrm{where} \mathrm{H}* \mathrm{is} \mathrm{excited} \mathrm{state} \mathrm{of} \mathrm{H} \mathrm{atoms} \\ \mathrm{where} \mathrm{the} \mathrm{electron} \mathrm{travels} \mathrm{in} \mathrm{orbit} \mathrm{whose} \mathrm{circumference} \mathrm{equal} \mathrm{to} \\ \mathrm{four} \mathrm{times} \mathrm{its} \mathrm{deBroglies}\text{'}\mathrm{s} \mathrm{wavelength}. \mathrm{Determine} \mathrm{the} \mathrm{least} \\ \mathrm{moles} \mathrm{of} \mathrm{X} \mathrm{that} \mathrm{would} \mathrm{be} \mathrm{required} : \\ \mathrm{Given} : \mathrm{I}.\mathrm{E}. \mathrm{of} \mathrm{H} =13.6\mathrm{eV}/\mathrm{atom}, \\ \mathrm{bond} \mathrm{energy} \mathrm{of} {\mathrm{H}}_2=4.526\mathrm{eV}/\mathrm{molecule}. \\ 1. 1 \\ 2. 2 \\ 3. 3 \\ 4. 4 \end{gathered}$$

$$\begin{gathered} For a 3s-orbital \\ \psi \left(3s\right)=\frac{1}{9\sqrt{3}}{\left(\frac{1}{a_0}\right)}^{3/2} \left(6-6\sigma +{\sigma }^2\right)e^{-\sigma /2}; where \sigma =\frac{2r.Z}{3a_0} \\ What is the maximum radial dis\tan ce of node from nucleus? \\ 1. \frac{\left(3+\sqrt{3}\right)a_{{0_{}}_{}}}{Z} \\ 2. \frac{a_0}{Z} \\ 3. \frac{3}{2}\frac{\left(3+\sqrt{3}\right)a_0}{Z} \\ 4. \frac{2a_0}{Z} \end{gathered}$$

Monochromatic radiation of specific wavelength is incident on H-atom in ground state. H-atom absorb energry 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

$In the graph between \sqrt{v} and Z for the mosley\text{'}s equation$
v  = aZ-b, the intercept OX is -1 on v  axis.
$$
       
What is the frequency when atomic number (Z) is 51?
$1. 50 s^{-1}$
$2. 100 s^{-1 }$
$3. 2500 s^{-1}$
$4. None of these$

Balmer gave an equation for wavelength of visible region of H-Spectrum as $\lambda =\frac{K{n}^2}{n^2-4}$
where n= principal quantum number of energy level, k = constant in terms of R (Rydberg constant).
The value of K in terms of R is :
1. R
2. $\frac{R}{2}$
3. $\frac{4}{R}$
4. $\frac{5}{R}$

Balmer gave an equation for wavelengh of visible region of H-spectrum as $\lambda =\frac{K{n}^2}{n^2-4}.$
$$\begin{gathered} Where n= principle quantum number of energy level, K=cons\tan t in terms of R (rydberg cons\tan t). \\ The value of k in terms of R is : \\ 1. R \\ 2. \frac{R}{2} \\ 3.\frac{4}{R} \\ 4. \frac{5}{R} \end{gathered}$$