1. When ana-particle ofmass mmoving with velocity v bombardson a heavy nucleus of charge Ze, itsdistance of closest approach fromthe nucleus depends on m as

(1).\(\displaystyle \frac{1}{\sqrt{m}}\)

(2). \(\displaystyle \frac{1}{m^2}\)

(3). \(m\)

(4). \(\displaystyle \frac{1}{m}\)

2. The total energy of an electron inthe nth stationary orbit of thehydrogen atomcan be obtained by

(1).\(\displaystyle E_n = \frac{13.6}{n^2}eV\)

(2). \(\displaystyle E_n = -\frac{13.6}{n^2}eV\)

(3). \(\displaystyle E_n = -\frac{1.36}{n^2}eV\)

(4). \(\displaystyle E_n = -13.6 x n^2eV\)

3. For which one of the following,Bohr model is not valid?

(1).Singly ionised helium atom (\(He^+\) )

(2). Deuteron atom

(3). Singly ionised neon atom (\(Ne^+\) )

(4). Hydrogen atom

4. The radius of the first permitted Bohr orbit for the electron, in a hydrogen atomequals 0.51 Å and its ground state energy equals −13.6 eV. If the electron in the hydrogen atomis replaced by muon (μ⁻¹ ) [Charge same as electron and mass 207 m_e ], the first Bohr radius and ground stateenergy will be

(1).0.53x10^-13m, -3.6 eV

(2). 25.6x10^-13m, -2.8 eV

(3). 2.56x10^-13m, -2.8 keV

(4). 2.56x10^-13m, -13.6 keV

5. The total energy of an electron inan atomin an orbit is −3 4 . eV.Its kinetic and potential energiesare, respectively:

(1).−3.4 eV, −6.8 eV

(2). 3.4 eV, −6.8 eV

(3). 3.4 eV, 3.4 eV

(4). −3.4 eV, −3.4 eV

6. The ratio of kinetic energy to thetotal energy of an electron in aBohr orbit of the hydrogen atom, is

(1).2 : − 1

(2). 1 : − 1

(3). 1:01

(4). 1 : −2

7. The ratio of wavelengths of the lastline of Balmer series and the lastline of Lyman series is

(1).2

(2). 1

(3). 4

(4). 0.5

8. If an electron in a hydrogen atomjumps fromthe 3rd orbit to the 2ndorbit, it emits a photon ofwavelength l.When it jumps fromthe 4th orbit to the 3rd orbit, thecorresponding wavelength of thephoton will be

(1).\(\displaystyle \frac{16}{25} \lambda \)

(2). \(\displaystyle \frac{9}{16} \lambda \)

(3). \(\displaystyle \frac{20}{7} \lambda \)

(4). \(\displaystyle \frac{20}{13} \lambda \)

9. Hydrogen atom in ground state is excited by a monochromatic radiation of \(\lambda = 975 \mathring{A} \). Number of spectral lines in the resulting spectrum emitted will be

(1).3

(2). 2

(3). 6

(4). 10

10. Given below are two statements :
Statement I : Atoms are electrically neutral as they contain equal number of positive and negative charges .
Statement II : Atoms of each element are stable and emit their characteristic spectrum .
In the light of the above statements, choose the most appropriate answer from the options given below :

(1).Statement I is correct but Statement II is incorrect .

(2). Statement I is incorrect but Statement II is correct .

(3). Both Statement I and Statement . II are correct .

(4). Both Statement I and Statement II are incorrect .

11. Match List I with List II

Choose the correct answer from the options given below

(1).A - IV , B - III , C - I , D - II

(2). A - I , B - II , C - III , D - IV

(3). A - II , B - I , C - IV , D - III

(4). A - III , B - IV , C - II , D - I

12. In hydrogen spectrum, the shortest wavelength in the Balmer series is \(\lambda\). The shortest wavelength in the Bracket series is

(1).\(4\, \lambda\)

(2). \(9\, \lambda\)

(3). \(16\, \lambda\)

(4). \(2\, \lambda\)

13. The radius of inner most orbit of hydrogen atom is \(\displaystyle 5.3 \times 10^{-11} \) m. What is the radius of third allowed orbit of hydrogen atom?

(1).\(\displaystyle 1.06\, \mathring{A} \)

(2). \(\displaystyle 1.59\, \mathring{A} \)

(3). \(\displaystyle 4.77\, \mathring{A} \)

(4). \(\displaystyle 0.53\, \mathring{A} \)

14. Let T1 and T2 be the energy of an electron in the first and second excited states of hydrogen atom, respectively. According to the Bohr’s model of an atom, the ratio T1 : T2 is :

(1).1:04

(2). 4:01

(3). 4:09

(4). 9 : 4

15. Given the value of Rydberg constant is \(10\,\text{m}^{-1}\), the wave number of the last line of the Balmer series in hydrogen spectrum will be

(1).\(0.5 \times 10^7\,\text{m}^{-1}\)

(2). \(0.25 \times 10^7\,\text{m}^{-1}\)

(3). \(2.5 \times 10^7\,\text{m}^{-1}\)

(4). \(0.025 \times 10^4\,\text{m}^{-1}\)

16. Consider \(3^{rd}\) orbit of \(\text{He}^+\) (Helium), using non-relativistic approach, the speed of electron in this orbit will be (given \(\text{K}\, =\,9 \times 10^9\) constant, \(\text{Z}\,=\,2\) and \(\text{h (Planck's constant)}\,=\,6.6 \times 10^{-34}Js\)

(1).\(2.92 \times 10^6\,m/s\)

(2). \(1.46 \times 10^6\,m/s\)

(3). \(0.73 \times 10^6\,m/s\)

(4). \(3.0 \times 10^8\,m/s\)

17. A particle of mass m is moving around the origin with a constant force F pulling it towards the origin. If Bohr model is used to describe its motion, the radius of the \(\text{n}^{\text{th}}\) orbit and the particle's speed v in the orbit depends on n as

(1).\(\text{r}\propto{n^{\frac{4}{3}}}\), \(\text{v}\propto{n^{-\frac{1}{3}}}\)

(2). \(\text{r}\propto{n^{\frac{1}{3}}}\), \(\text{v}\propto{n^{\frac{1}{3}}}\)

(3). \(\text{r}\propto{n^{\frac{1}{3}}}\), \(\text{v}\propto{n^{\frac{2}{3}}}\)

(4). \(\text{r}\propto{n^{\frac{2}{3}}}\), \(\text{v}\propto{n^{\frac{1}{3}}}\)

18. De-Broglie wavelength of an electron orbiting in the n = 2 state of hydrogen atom is close to (Given Bohr radius = 0.052 nm)

(1).2.67 nm

(2). 0.067 nm

(3). 0.67 nm

(4). 1.67 nm