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1. What is the kinetic energy of the electron in an orbit of radius \(r\) in the hydrogen atom?
(\(e\) = electronic charge)

1.	\(\dfrac{k e^{2}}{r^{2}}\)	2.	\(\dfrac{k e^{2}}{2 r}\)
3.	\(\dfrac{k e^{2}}{r}\)	4.	\(\dfrac{k e^{2}}{2 r^{2}}\)

2. The energy of \(24.6\) eV is required to remove one of the electrons from a neutral helium atom. What is the energy (in eV) required to remove both the electrons from a neutral helium atom?
1. \(38.2\)
2. \(49.2\)
3. \(51.8\)
4. \(79.0\)

3. The radius of a hydrogen atom in its ground state is \(5.3\times 10^{-11}\) m. After collision with an electron, it is found to have a radius of \(21.2\times 10^{-11}\) m. What is the principal quantum number n of the final state of the atom?
1. \(n=4\)
2. \(n=2\)
3. \(n=16\)
4. \(n=3\)

4.

When a hydrogen atom is raised from the ground state to excited state
1. both KE and PE increase
2. both KE and PE decrease
3. PE increases and KE decreases
4. PE decreases and KE increases

5.

In the Bohr's model of a hydrogen atom, the centripetal force is furnished by the Coulomb attraction between the proton and the electron.  If ${\alpha }_0$ is the radius of the ground state orbit, m is the mass and e is the charge on the electron, ${\epsilon }_0$ is the vaccum permittivity, the speed of the electron is  [1998]
1. zero         
2. $\frac{e}{\sqrt{{\epsilon }_0{a}_{0}m}}$
3. $\frac{e}{\sqrt{4{\mathrm{\pi \epsilon }}_0{\mathrm{a}}_0\mathrm{m}}}$ 
4. $\frac{\sqrt{4{\mathrm{\pi \epsilon }}_0{\mathrm{a}}_0\mathrm{m}}}{e}$

6.

If V be the accelerating voltage, then the maximum frequency of continuous x-rays is given by
1.  $\frac{eh}{V}$
2.  $\frac{hV}{e}$
3.  $\frac{eV}{h}$
4. $\frac{h}{eV}$

7.

Magnetic moment due to the motion of the electron in ${\mathrm{n}}^{\mathrm{th}}$  energy state of a hydrogen atom is proportional to
1.  n
2.  ${\mathrm{n}}^0$
3.  ${\mathrm{n}}^5$
4.  ${\mathrm{n}}^3$

8. A monochromatic radiation of \(\lambda = 975~\mathring{A}\) excites a hydrogen atom in its ground state. The number of spectral lines in the resulting spectrum emitted will be:
1. \(3\)
2. \(2\)
3. \(6\)
4. \(10\)

9.

The transition from the state n=3 to n=1
a hydrogen like atom results in ultraviolet
radiation. Infrared radiation will be obtained
in the transition from
(a) $2\to 1$
(b) $3\to 2$
(c) $4\to 2$
(d) $4\to 3$

10.

The figure indicates the energy level diagram of an atom and the origin of six spectral lines in emission (e.g. line no. 5 arises from the transition from level B to A). The following spectral lines will also occur in the absorption spectrum

(a) 1, 4, 6                      (b) 4, 5, 6
(c) 1, 2, 3                      (d) 1, 2, 3, 4, 5, 6

11.

An ionic atom equivalent to hydrogen atom has wavelength equal to 1/4 of the wavelengths of hydrogen lines. The ion will be 
(1) ${\mathrm{He}}^{+}$        
(2) ${\mathrm{Li}}^{++}$
(3) ${\mathrm{Ne}}^{9+}$       
(4) ${\mathrm{Na}}^{10+}$

12.

In hydrogen atom, if the difference in the energy of the electron in n =2 and n = 3 orbits is E, the ionization energy of hydrogen atom is 
(1) 13.2 E               
(2) 7.2 E
(3) 5.6 E                 
(4) 3.2 E

13. What is the ratio of the longest to shortest wavelengths in Brackett series of hydrogen spectra?

1.	\(\dfrac{25}{9}\)	2.	\(\dfrac{17}{6}\)
3.	\(\dfrac{9}{5}\)	4.	\(\dfrac{4}{3}\)

14. In a hypothetical Bohr hydrogen, the mass of the electron is doubled. What will be the energy \(E_0\) and the radius \(r_0\) of the first orbit?
\((a_0\) is the Bohr radius) 

1.	\(E_0=-27.2 ~\text{eV};~r_0={a}_0 / 2\)
2.	\(E_0=-27.2 ~\text{eV}; ~r_0={a}_0\)
3.	\(E_0=-13.6~\text{eV} ; ~r_0={a}_0 / 2\)
4.	\(E_0=-13.6 ~\text{eV}; ~r_0={a}_0\)

15. The electric potential between a proton and an electron is given by \(V = V_0\mathrm{Ln}\left(\frac{r}{r_0}\right)\) where \(r_0\) is a constant. Assuming Bohr’s model to be applicable, the variation of \(r_n\) with \(n\), \(n\) being the principal quantum number, is:
1. \(r_n \propto n\)
2. \(r_n \propto\frac{1}{n}\)
3. \(r_n\propto n^2\)
4. \(r_n \propto\frac{1}{n^2}\)