This assignment contain all important objective questions of atoms and nuclei , which is important for the students preparing for board examination and other competitive examinations .

Atomic Structure

1. According to Bohr’s atomic model:
   (a)an atom has heavy, positively charged nucleus
   (b)the electron radiates energy only when it jumps to another orbit
   (c)the electron can move only in particular orbits
   (d)all the above statements are correct

 

2. In an atom, two electrons move around the nucleus in circular orbit of radii R and 4R. The ratio of the time taken by them to complete one revolution is:
   (a)1/4            (b) 4/1                              (c) 8/1                            (d) 1/8

 

3. According to Bohr’s quantum condition, an electron can revolve only in those orbits in which:                 
   (a) its energy is an integral multiple of h/2π
   (b) its linear momentum is an integral multiple of h/2π
   (c)  its angular momentum is an integral multiple of h/2π
   (d) its angular momentum vector is perpendicular to magnetic dipole moment vector

 

4. According Bohr’s theory the radius of the electron in an orbit described by principal quantum number n and atomic number Z is proportional to:                                                                                   
   (a)Z²n²
   (b) Z² /n²
   (c) Z² /n
   (d) n² /Z

 

5. When the electron jumps from a level n = 4 to n = 1, the momentum of the recoiled hydrogen atom will be:                             
   (a)5 ₓ 10^-27 kg – ms^-1
   (b) 13.6 ₓ 10^-19 kg – ms^-1
   (c)75 ₓ 10^-19 kg – ms^-1
   (d) zero

 

6. The radius of Bohr’s fast orbit is a₀. The electron in nth orbit has a radius:
   (a)na₀
   (b) a₀/n
   (c) n²a₀
   (d) a₀/n²

 

7. The angular momentum of an electron in the nth orbit is given by:
   (a)nh
   (b) h/2πn
   (c) nh/2π
   (d) n²h/2π

 

8. When a hydrogen atom is raised from the ground state to fifth state:
   (a)both KE and PE increase
   (b) PE increases and KE decreases
   (c)both KE and PE decrease
   (d) PE decreases and KE increases
9. As the electron in Bohr orbit of hydrogen atom passes from state n = 2 to n = 1, the KE (K) and PE (U) change as:                                  (a)K two-fold, U also two-fold     
   (c) K four-fold, U two-fold
   (b)K four-fold, U also four-fold
   (d) K two-fold U four-fold
10.  An electron jumps from the 4^th orbit to the 2^nd orbit of a hydrogen atom. Given the Rydberg constant R = 10⁵ cm^-1, the frequency in Hz of the emitted radiation will be:                         
    (a)3/16 ₓ 10⁵
    (b) 3/16 ₓ 10¹⁵
    (c) 9/16 ₓ 10¹⁵
    (d) 3/4 ₓ 10¹⁵ 
11.  Nitrogen gas, cynogen gas and compounds of carbon give band spectra because:
    (a)these are excited in molecular state
    (b)these are in atomic state
    (c)these are inorganic compounds
    (d)these are in gaseous state
12.  The hydrogen atom can give spectral lines in the series, Lyman, Balmer and Paschen. Which of the following statements is correct?                                                                                                 
    (a)Lyman series is in the infrared region
    (b)Balmer series is in the visible region (partly)
    (c)Balmer series is solely in the ultraviolet region
    (d)Paschen series is in the visible region
13. .Which of the following statements is true regarding Bohr’s model of hydrogen atom?                                                               
    (a)Orbiting speed of electron decreases as it falls to discrete orbits away from the nucleus.
    (b)Radii of allowed orbits of electrons are proportional to the principal quantum number.
    (c)Frequency with which electrons orbits around the nucleus in discrete orbits is inversely proportional the principal quantum number.
14. Binding force with which the electron is bound to the nucleus increases as it shifts to outer orbits.
    
    (A)a and    c
    (B)   b    and    d
    (C)   a, b   and   c
    (D)   b, c   and   d
15.  An electron in the hydrogen atom jumps from excited state n to the ground state. The wavelength so emitted illuminates a photosensitive material having work function 2.75 eV. If the stopping potential of the photo-electron is 10 V, then the value of n is:
    (a)2                 (b)   3            (c)  4                   (d)   5
16.  In Bohr’s model, the atomic radius of the fast orbit is r₀;then the radius of the third orbit is:
    (a)r₀/9                        (b)  r₀                 (c) 9r₀                              (d) 3r₀ 
17.  The ground state energy of H-atom is 13.6 eV. The energy needed to ionise H-atom from its second excited state is:       (a)51 eV       (b) 3.4 eV               (c) 13.6 eV              (d) 12.1 eV
18. Hydrogen atoms are excited from ground state to the state of principal quantum number 4. Then, the number of spectral lines observed will be:                 
    (a) 3       (b)  6        (c) 5           (d)  2
19. If an electron in n = 3 orbit of hydrogen atom jumps down to n = 2 orbits, the amount of energy released and the wavelength of radiation emitted are:
    (a)85 eV, 6566 Å (b) 1.89eV, 1240 Å        (c) 1.89 eV, 6566 Å   (d) 1.5 eV,6566 Å
20.  The longest wavelength that a single ionised helium atom in its ground state will absorb is:       
    (a)912 Å            (b) 304 Å              (c) 606 Å            (d) 1216 Å
21.  If the ionisation potential of hydrogen atom is 13.6 eV, the energy required to remove the electron from the third orbit of hydrogen atom is:                 
    (a)5 V          (b) 1.5 eV          (c) 4.5 eV         (d) 3.4 V
22. The ratio of the areas within the electron orbits for the first excited state the ground state for the ground state for the hydrogen atom is:(a)2 : 1 (b) 4 : 1    (c) 8 : 1    (d) 16 : 1
23. The first excitation potential of the hydrogen atom in the ground state is:
    (a)6 volt (b) 10.2 volt (c) 3.4 volt     (d) 1.89 volt
24. The minimum energy in electron volt required to strip a ten times ionized sodium atom ( i.e., Z = 11) of its last electron is:
    (a)6 eV        (b) 13.6/11  eV    (c) 13.6 ₓ 11 eV      (d) 13.6 ₓ (11)² eV
25.  Of the following transitions in hydrogen atom, the one which gives emission line of minimum frequency is:(a)n = 1 to n = 2   (b) n = 3 to n = 10        (c) n = 10 to n = 3        (d) n = 2 to n = 1
26. The energy of an electron in the nth orbit of positronium is:
    (a) -13.6/n² eV (b) -13.6 ₓ 2/n² eV       (c) -13.6 ₓ 4/n² eV        (d) -13.6/2n² eV
27. The ratio (in SI units) of magnetic dipole moment to that of the angular momentum of electron of mass m kg and charge e coulomb in Bohr’s orbit of hydrogen atom is:
    (a) e/2m (b) e/m             (c) 2e/m        (d) none of these
28.  The Bohr model of atoms: 
    (a)assumes that the angular momentum of the electrons is quantized
    (b)uses Einstein’s photoelectric equation
    (c)predicts continuous emission spectra for atoms
    (d)predicts the same emission spectra for all types of atoms
29.  The angular momentum of an electron in a hydrogen atom is proportional to:
    (a)1/√r         (b) 1/r          (c) √r           (d) r² 
30.  What will be the angular momentum in fourth orbit, if L is the angular momentum of the electron in the second orbit of hydrogen atom? 
    (a)2 L (b) 3/2 L     (c) 2/3 L      (d) L/2
31.  The required energy to detach one electron from Balmer series of hydrogen spectrum is:     
    (a)6 eV        (b) 10.2 eV           (c) 3.4 eV    (d) -1.5 eV
32.  Which of the following is quantised according to Bohr’s theory of hydrogen atom?       (a)Linear momentum of electron
    (b)Angular momentum of electron
    (c)Angular velocity of electron
    (d)Linear velocity of electron
33. The energy levels of a certain atom for 1^st ,2^nd and 3^rd levels are E, 4E/3 and 2E respectively. A photon of wavelength λ is emitted for a transition 3 →1.What will be the wavelength of emission for transition 2 → 1?     
    (a) λ/3       (b) 4λ/3       (c) 3λ/4              (d) 3λ
34. The ratio of the frequencies of the long wavelength limits of the Lyman and Balmer series of hydrogen is: 
    (a)27 : 5 (b) 5 : 27    (c) 4 : 1    (d) 1 : 4
35. If electron in a hydrogen atom has moved from n = 1 to n = 10 orbit, the potential energy of the system has: 
    (a)Increased       (b)Decreased         (c) remains unchanged      (d) become zero
36. The energy of hydrogen atom in nth orbit is E_n , then the energy in nth orbit of singly ionised helium atom will be:     
    (a)4E_n     (b) E_n/4                 (c) 2E_n                      (d) E_n/2
37. The energy of hydrogen atom is -13.6 eV in the first orbit, then calculate the energy of He atom in the same orbit:   
    (a)6 eV        (b) -27.2 eV            (c) -54.4 eV           (d) +54.4 eV
38.  In hydrogen spectrum, the shortest wavelength in Balmer series is λ. The shortest wavelength in Brackett series will be:(a)2λ        (b) 4λ                            (c) 9λ                               (d) 16λ
39. The ratio of the largest to shortest wavelength in Lyman series of hydrogen spectra is:   
    (a) 25/9  (b) 17/6 (c) 9/5 (d) 4/3
40. The minimum orbital angular momentum of the electron in hydrogen atom is: 
    (a) h             (b) h/π                      (c) h/2π                       (d) h/2
41. The total energy of an electron in the first excited state of hydrogen atom is about – 3.4 eV. Its KE in this state is:
    (a)4 eV (b) 6.8 eV                      (c) -3.4 eV                       (d)-6.8 eV
42. The ground state energy of hydrogen atom is -13.6 eV. What is the potential energy of the electron in this state?
    (a)0 eV (b) -27.2 eV                  (c) 1 eV                            (d) 2 eV
43.  If λ₁ and λ₂ are the wavelengths of the first member of the Lyman and Paschen series respectively, then λ₁ : λ₂ is:   
    (a)1 : 3 (b) 1 : 30                       (c) 7 : 50                           (d) 7 : 108

 

 

Important questions of atoms and nuclei.

This topic is important for class 12th student . it is considered this chapter is little bit easier than other previous chapter of physics for board examination point of view . One important reason is that student already studied this chapter in class 11th (chemistry) , so it is easy to learn this chapter . Through “important questions of atoms and nuclei” ,  I am going to provide some important questions based on this topic . Student preparing for board examination of all board should revise all these questions given in ” important questions of atoms and nuclei”.

Here is some important questions of atoms and nuclei-

Atoms- nuclei

1. Draw a labelled diagram of alpha particle scattering experiment. Give Rutherford observations and discuss the significance of this experiment .
2. Using postulates of Bohr energy of hydrogen atom ,show that (a) the radii of orbits increases as n² and (b) the total energy of the electron increases as 1/n² , where n is the principle quantum number of the atom .
3. Draw a schematic arrangement of the Gieger -Marsden experiment for studying alpha particle scattering by a thin foil of gold . describe briefly , by drawing trajectories of the scattered alpha particle . haw this studies can be used to estimate the size of the nucleus ?

 

4. State any two postulates of Bohr theory of hydrogen atom . what is the maximum possible no. of spectral lines observed when the hydrogen atom is in its second exited state ? justify your answer . calculate the ratio of the max. and min. wavelength of the radiation emitted in this process.

 

5. Using Bohr postulates for hydrogen atom , show that the total energy of the electron in the stationary states can be expressed as the sum of kinetic energy(K) and potential energy (U) , where K=-2U. hence , deduce the expression for the total energy in the n^th energy level of hydrogen atom   .

 

6. The energy of an electron in the ground state of hydrogen atom is -13.6 Ev. (i) what does the negative sign signify ? (ii)how much energy is required to take an electron in this atom from the ground state to the first exited state?

 

 

7. In Bohr theory of hydrogen atoms, calculate the energy of the photon emitted during a transition of the electron from first exited state to its ground state . write in which region of the electromagnetic spectrum this transition lies. Given R=1.03 * 10⁷m^-1.
8. The electron in a given Bohr orbit has a total energy of -1.5Ev. calculate its(i) kinetic energy(ii)potential energy (iii) wavelength of the radiation emitted , when this electron makes a transition to the ground state.
9. The energy level diagram of an element is given below . identify using necessary calculations , which transition corresponds to the emission of the spectral line of wavelength 102.7 nm . which transition corresponds to the emission of radiation of maximum wavelength?

.

 

 

10. The ground state energy of hydrogen atom is -13.6 eV.  ( I ) What is the potential energy of an electron in the third exited state? (ii) what will be the maximum and minimum wavelength of the emitted  radiation of Lyman series of hydrogen spectrum.

 

11. State and explain the law of radioactive decay. Plot the graph of showing the number  (N)  of undecayed nuclei as a function of time (t) for a given radioactive sample having half life T_1/2.depict in the plot the number of undecayed nuclei at (i) t=3T_1/2­ (ii) t=5T_1/2.

 

12. How the size of nuclei is experimentally determined ? write the relation between the radius and mass number of the nucleus . show that the density of the nucleus is independent of its mass number. Two nuclei of mass number in the ratio 27:125. What is the ratio of their nuclear radius and , ratio of their densities.

 

13. (i)Define the activity of the radioactive material and write its SI unit. plot a graph showing the variation of activity with respect to time of a given radioactive sample.(ii) what is meant by half life time of a radioactive element ? the half life of a radioactive sample is 30s calculate (a) the decay constant and (b)time taken for the sample to decay by 3/4^thof the initial value .explain alpha , beta and , gama decay with an example . if an element ²³⁸X ₉₂ converted into another element ²²²Y₉₀ find the no of alpha and beta particles emitted.

 

14. Draw the binding energy per nucleon curve . using the curve state clearly how the release in energy in the process of nuclear fission and nuclear fusion can be explained.

 

15. Draw a plot of potential energy of a pair of nucleons , as a function of their separation . write two important conclusions which you can draw regarding the nature of nuclear force. Also, explain the mass of a nucleus , in the ground state is always less than total mass of its constituents neutron and proton .

 

16. We are given the following atomic masses ; ²³⁸ U₉₂ =238.05079u; ²³⁴ Th₉₀=234.04363u ; ²³⁷Pa₉₁=237.05121u; ¹H₁=1.00783u; ⁴He₂=4.00260 u ;(a) calculate the energy released during alpha decay of uranium (b) calculate the kinetic energy of alpha particle ,and (c) show that ; ²³⁸ U₉₂ cannot spontaneously emit a proton.

 

17. The activity of a radioactive sample drop to 1/16 ^th of its initial value in 32 years . find the mean life of the sample .