MCQ July-22
Video Lecture for Solutions
Question 1: An `\alpha` particle and a proton are accelerated from rest through the same potential difference. The ratio of linear momenta acquired by above two particles will be:
(a) `\sqrt{2}:1`
(b) `2\sqrt{2}:1`
(c) `4\sqrt{2}:1`
(d) `8:1`
Answer: (b)
Question 2: Find the ratio of energies of photons produced due to transition of an electron of hydrogen atom from its (i) second permitted energy level to the first level, and (ii) the highest permitted energy level to the first permitted level.
(a) `3:4`
(b) `4:3`
(c) `1:4`
(d) `4:1`
Answer (a)
Question 3: The equation `\lambda=\frac{1.227}{x}nm`can be used to find the de-Brogli wavelength of an electron. In this equation `x` stands for :
Where
`m=`mass of electron
`P=`momentum of electron
`K=`Kinetic energy of electron
`V=`Accelerating potential in volts for electron
(a) `\sqrt{mK}`
(b) `\sqrt{P}`
(c) `\sqrt{K}`
(d) `\sqrt{V}`
Answer (d)
Question 4: The ratio of wavelengths of proton and deuteron accelerated by potential `V_{p}`and `V_{d}` is `1 : \sqrt{2}`. Then the ratio of `V_{p}` to `V_{d}` will be :
(a) `1:1`
(b) `\sqrt{2}:1`
(c) `2:1`
(d) `4:1`
Answer (d)
Question 5: Hydrogen atom from excited state comes to the ground state by emitting a photon of wavelength `\lambda`. The value of principal quantum number `'n'` of the excited state will be : (`R:` Rydberg constant)
(a) `\sqrt{\frac{\lambda R}{\lambda-1}}`
(b) `\sqrt{\frac{\lambda R}{\lambdaR-1}}`
(c) `\sqrt{\frac{\lambda }{\lambdaR-1}}`
(d) `\sqrt{\frac{\lambda R^{2}}{\lambdaR-1}}`
Answer (b)
Question 6: The momentum of an electron revolving in `n^{th}` orbit is given by :
(Symbols have their usual meanings)
(a) `\frac{nh}{2\pi r}`
(b) `\frac{nh}{2r}`
(c) `\frac{nh}{2\pi}`
(d) `\frac{2\pi r}{nh}`
Answer (a)
JUNE-22 Session
(Take : `e=1.6\times10^{-19}C, m_{p}=1.67\times10^{-27}kg`)
(a) `7.4MeV`
(b) `14.86MeV`
(c) `7.4GeV`
(d) `704GeV`
Answer (a)
Question 8: A hydrogen atom in ground state absorbs `12.09 eV` of energy. The orbital angular momentum of the electron is increased by :
(a) `1.05\times10^{-34}Js`
(b) `2.11\times10^{-34}Js`
(c) `3.16\times10^{-34}Js`
(d) `4.22\times10^{-34}Js`
Answer (b)
Question 9: A hydrogen atom in its ground state absorbs `10.2 eV` of energy. The angular momentum of electron of the hydrogen atom will increase by the value of :
(Given, Planck's constant `= 6.6\times10^{-34} Js`).
(a) `2.10\times10^{-34}Js`
(b) `1.05\times10^{-34}Js`
(c) `3.15\times10^{-34}Js`
(d) `4.2\times10^{-34}Js`
Answer (b)
Question 10: Which of the following figure represents the variation of `ln(\frac{R}{R_{o}})` with `lnA`(if `R` = radius of a nucleus and `A` = its mass number)
Answer (B)
Question 11: The ratio for the speed of the electron in the `3^{rd}` orbit of `He^+` to the speed of the electron in the `3^{rd}` orbit of hydrogen atom will be :
(a) `1:1`
(b) `1:2`
(c) `4:1`
(d) `2:1`
Answer (d)
Question 12: In Bohr's atomic model of hydrogen, let `K`, `P` and `E` are the kinetic energy, potential energy and total energy of the electron respectively. Choose the correct option when the electron undergoes transitions to a higher level :
(a) All K, P and E increase.
(b) K decreases, P and E increase.
(c) P decreases, K and E increase.
(d) K increases, P and E decrease.
Answer (b)
Question 13: Choose the correct option from the following options given below :
(a) In the ground state of Rutherford's model electrons are in stable equilibrium. While in Thomson's model electrons always experience a net-force.
(b) An atom has a nearly continuous mass distribution in a Rutherford's model but has a highly non-uniform mass distribution in Thomson's model.
(c) A classical atom based on Rutherford's model is doomed to collapse.
(d) The positively charged part of the atom possesses most of the mass in Rutherford's model but not in Thomson's model.
Answer (c)
AUG-21
Question 14: A particular hydrogen like ion emits radiation of frequency `2.92 \times 10^{15} Hz` when it makes transition from `n = 3` to `n = 1`. The frequency in `Hz` of radiation emitted in transition from `n = 2` to `n = 1` will be :
(a) `0.44 \times 10^{15}`
(b) `6.57 \times 10^{15}`
(c) `4.38 \times 10^{15}`
(d) `2.46 \times 10^{15}`
Correct answer: (d)
Question 15: An electron and proton are separated by a large distance. The electron starts approaching the proton with energy `3 eV`. The proton captures the electron and forms a hydrogen atom in second excited state. The resulting photon is incident on a photosensitive metal of threshold wavelength `4000 A^\circ`. What is the maximum kinetic energy of the emitted photo-electron?
Question 15: An electron and proton are separated by a large distance. The electron starts approaching the proton with energy `3 eV`. The proton captures the electron and forms a hydrogen atom in second excited state. The resulting photon is incident on a photosensitive metal of threshold wavelength `4000 A^\circ`. What is the maximum kinetic energy of the emitted photo-electron?
(a) `7.61 eV`
(b) `1.41 eV`
(c) `3.3 eV`
(d) No photo-electron would be emitted
Correct answer: (b)
Correct answer: (b)
Question 16: Consider the following statements :
A. Atoms of each element emit characteristics spectrum.
B. According to Bohr's Postulate, an electron in a hydrogen atom, revolves in a certain stationary orbit.
C. The density of nuclear matter depends on the size of the nucleus.
D. A free neutron is stable but a free proton decay is possible.
E. Radioactivity is an indication of the instability of nuclei.
Choose the correct answer from the options given below :
(a) A, B, C, D and E
(b) A, B and E only
(c) B and D only
(d) A, C and E only
Correct answer: (b)
March 2021 Session
Question 17: Imagine that the electron in a hydrogen atom is replaced by a muon (`\mu`). The mass of muon particle is `207` times that of an electron and charge is equal to the charge of an electron. The ionization potential of this hydrogen atom will be :
(a) `13.6 eV`
(b) `2815.2 eV`
(c) `331.2 eV`
(d) `27.2 eV`
Correct answer: (b)
Question 18: The atomic hydrogen emits a line spectrum consisting of various series. Which series of hydrogen atomic spectra is lying in the visible region?
(a) Brackett Series
(b) Balmer Series
(c) Paschen Series
(d) Lyman Series
Correct answer: (b)
Question 19: If an electron is moving in the `n^{th}` orbit of the hydrogen atom, then its velocity `(v_n)` for the `n^{th}` orbit is given as :
(a) `v_n \propto \frac{1}{n}`
(b) `v_n \propto n^2`
(c) `v_n \propto n`
(b) `v_n \propto n^2`
(c) `v_n \propto n`
(d) `v_n \propto \frac{1}{n^2}`
Correct answer: (a)
Correct answer: (a)
Question 20: Which level of the single ionized carbon has the same energy as the ground state energy of hydrogen atom?
(a) `8`
(a) `8`
(b) `6`
(c) `1`
(d) `4`
Correct answer: (b)
Correct answer: (b)
February 2021 Session
Question 21: If `\lambda_1` and `\lambda_2` are the wavelengths of the third member of Lyman and first member of the Paschen series respectively, then the value of `\lambda_1 : \lambda_2` is :
(a) `7:135`
(b) `7:108`
(c) `1:9`
(d) `1:3`
Correct answer: (a)
Question 22: An electron of mass `m_e` and a proton of mass `m_p = 1836 m_e` are moving with the same speed. The ratio of their de Broglie wavelength `\frac{\lambda_e}{\lambda_p}` will be :
(a) `1`
(2) `1836`
(3) `\frac{1}{1836}`
(d) `918`
Correct answer: (b)
Correct answer: (b)
Question 23: In the given figure, the energy levels of hydrogen atom have been shown along with some transitions marked A, B, C, D and E.
The transitions A, B and C respectively represent :
(a) The ionization potential of hydrogen, second member of Balmer series and third member of Paschen series.
(b) The first member of the Lyman series, third member of Balmer series and second member of Paschen series.
(c) The series limit of Lyman series, third member of Balmer series and second member of Paschen series.
(d) The series limit of Lyman series, second member of Balmer series and second member of Paschen series.
Correct answer: (c)
September 2020 Session
Question 24: The radius R of a nucleus of mass number A can be estimated by the formula `R = (1.3 \times 10^{–15})A^{\frac{1}{3}} m`.
It follows that the mass density of a nucleus is of the order of :
(a) `10^{24} kg m^{-3}`
(b) `10^{10} kg m^{-3}`
(c) `10^{17} kg m^{-3}`
(d) `10^{3} kg m^{-3}`
Correct answer: (c)
Question 25: Hydrogen ion and singly ionized helium atom are accelerated, from rest, through the same potential difference. The ratio of final speeds of hydrogen and helium ions is close to :
(a) `2:1`
(b) `1:2`
(c) `5:7`
(d) `10:7`
Correct answer: (a)
Question 26: In a hydrogen atom the electron makes a transition from `(n + 1)^{th}` level to the `n^{th}` level. If `n >> 1`, the frequency of radiation emitted is proportional to :
(a) `\frac{1}{n}`
(b) `\frac{1}{n^2}`
(c) `\frac{1}{n^3}`
(d) `\frac{1}{n^4}`
Correct answer: (c)
January 2020 Session
Question 27: The graph which depicts the results of Rutherford gold foil experiment with `\alpha`-particles is :
`\theta`: Scattering angle
Y : Number of scattered `\alpha`-particles detected (Plots are schematic and not to scale)
Correct answer: (c)
(a) `5.6 \times 10^{12}`
(b) `1.6 \times 10^{14}`
(c) `7.8 \times 10^{14}`
(d) `6.2 \times 10^{15}`
Correct answer: (c)
Question 29: The electron in a hydrogen atom first jumps from the third excited state to the second excited state and subsequently to the first excited state. The ratio of the respective wavelengths, `\frac{\lambda_1}{\lambda_2}`, of the photons emitted in this process is :
(a) `\frac{22}{5}`
(b) `\frac{7}{5}`
(a) `\frac{22}{5}`
(b) `\frac{7}{5}`
(c) `\frac{9}{7}`
(d) `\frac{20}{7}`
Correct answer: (d)
Numerical:
Question 30: In the hydrogen spectrum, `\lambda` be the wavelength of first transition line of Lyman series. The wavelength difference will be `"a \lambda''` between the wavelength of `3^{rd}` transition line of Paschen series and that of `2^{nd}`transition line of Balmer series where `a=`___________.
Correct answer: 5
Question 31: `\frac{x}{x+4}` is the ratio of energies of photons produced due to transition of an electron of hydrogen atom from its
(i) third permitted energy level to the second level and
(ii) the highest permitted energy level to the second permitted level.
The value of `x` will be ____________.
Correct answer: 5
Question 32: A hydrogen atom in its first excited state absorbs a photon of energy `x \times 10^{-2} eV` and excited to a higher energy state where the potential energy of electron is `1.08 eV`. The value of `x` is ______________.
Correct answer: 286
Question 33: `\sqrt{d_1}` and `\sqrt{d_2}` are the impact parameters corresponding to scattering angles `60^{\circ}` and `90^{\circ}` respectively, when an `\alpha` particle is approaching a gold nucleus. For `d_1 = x d_2`, the value of `x` will be ____________.
Correct answer: 3
Question 34: `X` different wavelengths may be observed in the spectrum from a hydrogen sample if the atoms are exited to states with principal quantum number `n = 6` ? The value of `X` is ______________.
Correct answer: 15
Question 35: In Bohr's atomic model, the electron is assumed to revolve in a circular orbit of radius `0.5 A^{\circ}`. If the speed of electron is `2.2 \times 10^6 m/s`, then the current associated with the electron will be _____________ `10^{-2} mA`. [Take `\pi` as `\frac{22}{7}`]
Correct answer: 112
Question 36: A particle of mass `m` moves in a circular orbit in a central potential field `U(r) = U_0r^4`. If Bohr's quantization conditions are applied, radii of possible orbitals `r_n` vary with `n^{\frac{1}{\alpha}}`, where `\alpha` is ____________.
Correct answer: 3
Question 37: The first spectral lines of H-atom in the Balmer series are
given `\lambda_1, \lambda_2, \lambda_3` considering the Bohr atomic model, the wave lengths of first and third spectral lines `(\frac{\lambda_1}{\lambda_3})` are related by a factor of approximately `'x' \times 10^{-1}`.
The value of `x`, to the nearest integer, is _________.
Correct answer: 15
Question 38: The first member of the Balmer series of hydrogen atom has a wavelength of `6561 Å`. The wavelength of the second member of the Balmer series (in `nm`) is:
Correct answer: 486
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