Q.1. The number of orbitals associated with quantum number n = 5, m_{s }= +1/2 is (2020)
(1) 11
(2) 25
(3) 50
(4) 15
Ans. (2)
For principle quantum number (n) = 5, total of 5 subshells are associated that is s, p, d, f and gsubshells. Each orbital has two spin quantum number (m_{s}) = + 1/2 and 1/2. Thus, number of orbitals associated with n = 5 and m_{s }=_{ }+ 1/2 are equal to the number of orbitals in 5^{th} shell.
Q.2. For the Balmer series in the spectrum of H atom, the correct statements among (I) to (IV) are (2020)
(I) As wavelength decreases, the lines in the series converge
(II) The integer n_{1} is equal to 2
(III) The lines of longest wavelength correspond to n_{2} = 3
(IV) The ionization energy of hydrogen can be calculated from wave number of these lines
(1) (I), (III), (IV)
(2) (I), (II), (III)
(3) (I), (II), (IV)
(4) (II), (III), (IV)
Ans. (2)
For Balmer series in hydrogen spectrum, as the wavelength decreases, the lines in the series get converge. For Balmer series, n_{1} is 2 and for longest wavelength n_{2} is 3.
Q.3. The radius of the second Bohr orbit, in terms of the Bohr radius, a_{0}, in Li^{2+} is (2020)
(1) 2a_{0}/9
(2) 4a_{0}/9
(3) 4a_{0}/3
(4) 2a_{0}/9
Ans. (3)
We know,
Radius of Bohr’s orbit = a_{0}n^{2}/Z
For Li^{2+} (Z = 3), the radius of second orbit
Q.4. The de Broglie wavelength of an electron in the 4^{th} Bohr orbit is (2020)
(1) 2πa_{0}
(2) 4πa_{0}
(3) 6πa_{0}
(4) 8πa_{0}
Ans. (4)
From the relation,
2πr = nλ
For hydrogen atom,
⇒ λ = 8πa_{0}
Q.5. For emission line of atomic hydrogen from n_{i} = 8 to n_{f }= n, the plot of wave number against (1/n^{2}) will be (The Rydberg constant, R_{H} is in wave number unit) (2019)
(1) Linear with intercept  R_{H}
(2) Non linear
(3) Linear with slope R_{H}
(4) Linear with slope  R_{H}
Ans. (4)
As we know,
After putting the values, we get
Comparing to y = mx + c, we get
Q.6. Which of the following combination of statements is true regarding the interpretation of the atomic orbitals?
(a) An electron in an orbital of high angular momentum stays away from the nucleus than an electron in the orbital of lower angular momentum.
(b) For a given value of the principal quantum number, the size of the orbit is inversely proportional to the azimuthal quantum number.
(c) According to wave mechanics, the ground state angular momentum is equal to h/2π
(d) The plot of ψ vs r for various azimuthal quantum numbers, shows peak shifting towards higher r value. (2019)
(1) (a), (d)
(2) (a), (b)
(3) (a),(c)
(4) (b), (c)
Ans. (1)
(a) Angular momentum (L) = nh/2π
Therefore, as n increases, L also increases.
(b)
(c) For n = 1, L = 4/2π
(d) As l increases, the peak of ψ vs r shifts towards higher 'r' value.
Q.7. Which of the graphs shown below does not represent the relationship between incident light and the electron ejected from metal surface? (2019)
(1)
(2)
(3)
(4)
Ans. (3)
K.E. = hv  hv_{0}
where, v = Frequency of incident radiation
v_{0} = Threshold frequency
KE is independent of intensity, it depends on frequency of light. Intensity is directly proportional to the no. of electrons emitted.
Q.8. The ground state energy of hydrogen atom is 13.6 eV. The energy of second excited state of He^{+} ion in eV is: (2019)
(1) 54.4
(2) 3.4
(3) 6.04
(4) 27.2
Ans. (3)
According to Bohr’s model energy in n^{th} state
For second excited state, of He^{+}, n = 3
Q.9. Heat treatment of muscular pain involves radiation of wavelength of about 900 nm. Which spectral line of Hatom is suitable for this purpose?
[R_{H} = 1 x 10^{5} cm^{1}. h = 6.6 x 10^{34} Js, c = 3 x 10^{8} ms^{1}] (2019)
(1) Paschen,∞ → 3
(2) Paschen, 5 → 3
(3) Balmer, ∞ → 2
(4) Lyman, ∞ → 1
Ans. (1)
Q.10. The de Broglie wavelength (λ) associated with a photoelectron varies with the frequency (v) of the incident radiation as, [v_{0} is threshold frequency]: (2019)
(1)
(2)
(3)
(4)
Ans. (4)
According to deBroglie wavelength equation,
According to photoelectric effect,
Q.11. What is the work function of the metal if the light of wavelength 4000 Å generates photoelectrons of velocity 6 x 10^{5} ms^{1} from it? (2019)
(Mass of electron= 9 x 10^{31} kg
Velocity of light = 3 x 10^{8} ms^{1}
Planck’s constant= 6.626 x 10^{34} Js
Charge of electron = 1.6 x 10^{19} JeV^{1})
(1) 0.9 eV
(2) 3.1 eV
(3) 2. leV
(4) 4.0 eV
Ans. (3)
According to photoelectric effect,
Q.12. If the de Broglie wavelength of the electron in n^{th} Bohr orbit in a hydrogenic atom is equal to 1.5 πa_{0} (a_{0} is Bohr radius), then the value of n/z is: (2019)
(1) 0.40
(2) 1.50
(3) 1.0
(4) 0.75
Ans. (4)
Q.13. The quantum number of four electrons are given below:
I. n = 4, l = 2, m_{1} = 2, m_{s} = 1/2
II. n = 3, l = 2, m_{1}= 1, m_{s }= + 1/2
III. n = 4, l = 1, m_{1} = 0, m_{s} = + 1/2
IV. n = 3, l= 1, m_{1}= 1, m_{s} =  1/2
The correct order of their increasing energies will be: (2019)
(1) IV<III<II<I
(2) I<II<III<IV
(3) IV<II<III<I
(4) I<III<II<IV
Ans. (3)
The energy of an atomic orbital increases with increasing n + l. For identical values of n + l, energy increases with increasing n. Therefore the correct order of energy is:
Q.14. If p is the momentum of the fastest electron ejected from a metal surface after the irradiation of light having wavelength λ, then for 1.5p momentum of the photoelectron, the wavelength of the light should be:
(Assume kinetic energy of ejected photoelectron to be very high in comparison to work function): (2019)
Ans. (4)
In photoelectric effect,
Given that KE of ejected photoelectron is very high in comparison to work function w.
New wavelength
Q.15. For any given series of spectral lines of atomic hydrogen, let be the difference in maximum and minimum frequencies in cm^{1}. The ratio of is: (2019)
(1) 4 : 1
(2) 9 : 4
(3) 5 : 4
(4) 27 : 5
Ans. (2)
Q.16. Which one of the following about an electron occupying the 1s orbital in a hydrogen atom is incorrect? (The Bohr radius is represented by a_{0}).
(1) The probability density of finding the electron is maximum at the nucleus.
(2) The electron can be found at a distance 2a_{0} from the nucleus.
(3) The magnitude of the potential energy is double that of its kinetic energy on an average.
(4) The total energy of the electron is maximum when it is at a distance a_{0} from the nucleus. (2019)
Ans. (4)
The total energy of the electron is minimum at a distance of a_{0} from the nucleus for 1s orbital.
Q.17. The graph between ψ^{2} and r (radial distance) is shown below. This represents: (2019)
(1) 3s orbital
(2) 2s orbital
(3) 1s orbital
(4) 2p orbital
Ans. (2)
The given probability density curve is for 2s orbital due to the presence of only one radial node. 1s and 2p orbital do not have any radial node and 3s orbital has two radial nodes. Hence, option (2) is correct.
Q.18. The isoelectronic set of ions is: (2019)
(1) N^{3}, O^{2}, F^{} and Na^{+}
(2) N^{3} Li^{+}, Mg^{2+} and O^{2}
(3) F^{}, Li^{+}, Na^{+} and Mg^{2+}
(4) Li^{+}, Na^{+}, O^{2} and F^{}
Ans. (1)
Atomic numbers of N, O, F and Na are 7, 8, 9 and 11 respectively. Therefore, total number of electrons in each of N^{3}, O^{2}, F^{}, and Na^{+} are 10 and hence they are isoelectronic.
Q.19. The ratio of the shortest wavelength of two spectral series of hydrogen spectrum is found to be about 9. The spectral series are: (2019)
(1) Lyman and Paschen
(2) Balmer and Brackett
(3) Brackett and P fund
(4) Paschen and P fund
Ans. (1)
For determined shortest wavelength, n_{2} = ∞
Q.20. The group number, number of valence electrons, and valency of an element with atomic number 15, respectively, are: (2019)
(1) 16, 5 and 2
(2) 15, 5 and 3
(3) 16, 6 and 3
(4) 15, 6 and 2
Ans. (2)
Phosphorus has atomic number 15. Its group number is 15, number of valence electrons is 5 and valency is 3.
Q.21. The electrons are more likely to be found: (2019)
(1) in the region a and c
(2) in the region a and b
(3) only in the region a
(4) only in the region c
Ans. (1)
Probability of finding an electron will have maximum value at both 'a' and 'c'. There is zero probability of finding an electron at 'b'.
Q.22. Ejection of the photoelectron from metal in the photoelectric effect experiment can be stopped by applying 0.5 V when the radiation of 250 nm is used. The work function of the metal is: (2018)
(1) 4.5 eV
(2) 4 eV
(3) 5.5 eV
(4) 5 eV
Ans. (1)
Q.23. Which of the following statements is false? (2018)
(1) Splitting of spectral lines in electrical field is called Stark effect
(2) Frequency of emitted radiation from a black body goes from a lower wavelength of higher wavelength as the temperature increases
(3) Photon has momentum as well as wavelength
(4) Rydberg constant has unit of energy
Ans. (2, 4)
When temperature is increased, black body emit high energy radiation, from higher wavelength to lower wavelength.
Rydberg constant has unit length^{–1} (i.e. cm^{–1})
Q.24. The radius of the second Bohr orbit for hydrogen atom is
(Planck's Const. h = 6.6262 × 10^{–34} Js;
mass of electron = 9.1091 × 10^{–31} kg;
charge of electron e = 1.60210 × 10^{–19} C;
permittivity of vacuum ε_{0} = 8.854185 × 10^{–12} kg^{–1} m^{–3} A^{2}) (2017)
(1) 1.65 Å
(2) 4.76 Å
(3) 0.529 Å
(4) 2.12 Å
Ans. (4)
Q.25. If the shortest wavelength in Lyman series of hydrogen atom is A, then the longest wavelength in Paschen series of He^{+} is: (2017)
(1) 5A/9
(2) 36A/7
(3) 36A/5
(4) 9A/5
Ans. (2)
Shortest wavelength is corresponding to best ine
∴ n_{L} = 1 (Lyman series)
n_{H} = ∞ (infinite)
Q.26. The electron in the hydrogen atom undergoes transition from higher orbitals to orbital of radius 211.6 pm. This transition is associated with: (2017)
(1) Lyman series
(2) Balmer series
(3) Brackett series
(4) Paschen series
Ans. (2)
R = 211.6 pm = 2.11 Å
R = 0.529 x n^{2}/Z = 2.11 Å
n^{2} = 4 ⇒ n = 2
Q.27. A stream of electrons from a heated filament was passed between two charged plates kept at a potential difference V esu. If e and m are charge and mass of an electron, respectively, then the value of h/l (where l is wavelength associated with electron wave) is given by: (2016)
(1) me V
(2) 2me V
(3)
(4)
Ans. (4)
Q.28. The total number of orbitals associated with the principal quantum number 5 is: (2016)
(1) 5
(2) 20
(3) 25
(4) 10
Ans. (3)
Given, n = 5
Possible subshells are
5s, 5p, 5d, 5f, 5g
Total number of orbital = 1 + 3 + 5 + 7 + 9 = 25
Q.29. Aqueous solution of which salt will not contain ions with the electronic configuration 1s^{2} 2s^{2} 2p^{6} 3s^{2} 3p^{6}? (2016)
(1) NaCl
(2) CaI_{2}
(3) NaF
(4) KBr
Ans. (3)
NaF: Na^{+} = 1s^{2 }2s^{2 }2p^{6}
F^{–} = 1s^{2 }2s^{2 }2p^{6}
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