Atoms PYQs Set 10 (PDF)

Set 10 of 16 · Questions 271-300 of 453

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Mere Teacher · Previous Year Questions JEE Main Physics · Atoms · Set 10 (Q271-300)
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271. $Assuming the atom is in the ground state, the expression for the magnetic field at a point nucleus in hydrogen atom due to circular motion of electron is (μ_{0} \to permeability of free space, m \to mass of electron ϵ_{0} \to permittivity of free space, h \to Planck ’ s constant)$ (1) $\frac{μ _{0} e ^{3} π m ^{2}}{8 ϵ _{0}^{2} h ^{4}}$ (2) $\frac{μ _{0} e ^{2} π m ^{4}}{6 ϵ _{0}^{3} h ^{4}}$ (3) $\frac{μ _{0} e ^{7} π m ^{2}}{8 ϵ _{0}^{3} h ^{5}}$ (4) $\frac{μ _{0} e ^{3} π m ^{3}}{6 ϵ _{0}^{3} h ^{3}}$ 272. $Particle A of mass m_{A} = \frac{m}{2} moving along the x -axis with velocity v_{0} collides elastically with another particle B at rest having mass m_{B} = \frac{m}{3} . If both particles move along the x-axis after the collision, the change ∆ ⋋ in de-Broglie wavelength of particle A, in terms of its de-Broglie wavelength (⋋_{0}) before collision is:$ (1) $∆ ⋋ = 2 ⋋_{0}$ (2) $∆ ⋋ = 4 ⋋_{0}$ (3) $∆ ⋋ = \frac{3}{2} ⋋_{0}$ (4) $∆ ⋋ = \frac{5}{2} ⋋_{0}$ 273. $The time period of revolution of electron in its ground state orbit in a hydrogen atom is 1.6 \times 10^{-}^{16} s . The frequency of revolution of the electron in its first excited state (in s^{- 1}) is :$ (1) $6.2 \times 10^{15}$ (2) $5.6 \times 10^{12}$ (3) $7.8 \times 10^{14}$ (4) $1.6 \times 10^{14}$ 274. $The energy of an electron in an orbit of the Bohr's atom is - 0.04 E_{0} eV where E_{0} is the ground state energy. If L is the angular momentum of the electron in this orbit and h is the Planck's constant, then \frac{2 πL}{h} is____:$ (1) $5$ (2) $6$ (3) $2$ (4) $4$ 275. $The momentum of an electron revolving in n^{t h} orbit is given by: (Symbols have their usual meanings)$ (1) $\frac{nh}{2 πr}$ (2) $\frac{nh}{2 r}$ (3) $\frac{nh}{2 π}$ (4) $\frac{2 πr}{nh}$ 276. $The ionisation energy of an electron in the ground state of helium atom is 24.6 eV . The energy required to remove both the electron is$ (1) $51.8 eV$ (2) $79 eV$ (3) $38.2 eV$ (4) $49.2 cV$ 277. $What is the energy of the electron revolving in third orbit expressed in eV ?$ (1) $4.53 eV$ (2) $1.51 eV$ (3) $4 eV$ (4) $3.4 eV$ 278. $Frequency of revolution of an electron revolving in n^{th} orbit of H -atom is proportional to$ (1) $n independent of n$ (2) $1/ n^{2}$ (3) $1/ n^{3}$ (4) $n$ 279. $Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R Assertion A: The Bohr model is applicable to hydrogen and hydrogen-like atoms only. Reason R : The formulation of Bohr model does not include repulsive force between electrons. In the light of the above statements, choose the correct answer from the options given below$ (1) $A is true but R is false$ (2) $Both A and R are true and R is the correct explanation of A$ (3) $A is false but R is true$ (4) $Both A and R are true but R is NOT the correct explanation of A$ 280. $If a source of power 4 kW produces 10^{20} photons/second, the radiation belongs to a part of the spectrum called :$ (1) $X-rays$ (2) $ultraviolet rays$ (3) $microwaves$ (4) $γ -rays$ 281. $The nucleus_{50}^{120} X undergoes the series of reactions given below:_{X}^{A} Z \to α - decay P \to β - decay Q \to α - decay R The number of neutrons in the nucleus R is$ (1) $A - 5$ (2) $A - Z - 5$ (3) $A - 9$ (4) $A - Z - 4$ 282. $When the electron in hydrogen atom jumps from fourth Bohr orbit to second Bohr orbit, one gets the$ (1) $second line Balmer series$ (2) $first line of Balmer series$ (3) $first line of P fund series$ (4) $second line of Paschen series.$ 283. $The energy of hydrogen atom in n^{th} orbit is E_{n} then the energy in n^{th} orbit of singly ionised helium atom will be$ (1) $4 E_{n}$ (2) $E_{n} /4$ (3) $2 E_{n}$ (4) $E_{n} /2$ 284. $The atomic mass of_{6} C^{12} is 12.000000 u and that of_{6} C^{13}, is 13.003354 u . The required energy to remove a neutron from_{6} C^{13}, if mass of neutron is 1.008665 u, will be :$ (1) $62.5 MeV$ (2) $6.25 MeV$ (3) $4.95 MeV$ (4) $49.5 MeV$ 285. $The threshold wavelength of a photosensitive material is equal to the frequency of H_{a} line of hydrogen. If a photon whose frequency equal to the frequency of H_{b} line of hydrogen is incident on this photosensitive material, the maximum kinetic energy of the emitted photoelectrons is (R-Rydberg's constant, h- Planck's constant and c- speed of light in vacuum)$ (1) $Rhc$ (2) $\frac{5 R h c}{144}$ (3) $\frac{7 R h c}{144}$ (4) $\frac{Rh h}{36}$ 286. $Which of the following nuclear fragments corresponding to nuclear fission between neutron (_{0}^{1} n) and uranium isotope (_{92}^{235} U) is correct:$ (1) $_{56}^{144} Ba +_{36}^{89} Kr + 4_{0}^{1} n$ (2) $_{56}^{144} Ba +_{36}^{89} Kr + 3_{0}^{1} n$ (3) $_{56}^{140} Xe +_{38}^{94} Sr + 3_{0}^{1} n$ (4) $_{51}^{153} Sb +_{41}^{99} Nb + 3_{0}^{1} n$ 287. $A H e^{+} ion is in its first excited state. Its ionization energy is:$ (1) $48.36 eV$ (2) $54.40 eV$ (3) $13.60 eV$ (4) $6.04 eV$ 288. $In a hydrogen like ion, the energy difference between the 2^{nd} excitation energy state and ground is 108.8 eV. The atomic number of the ion is:$ (1) $1$ (2) $4$ (3) $3$ (4) $2$ 289. $As the quantum number increases, the difference in energy between consecutive energy levels$ (1) $Remains the same$ (2) $Increases$ (3) $Decreases$ (4) $Sometimes increases and sometimes decreases$ 290. $An electron in hydrogen atom makes a transition n_{1} \to n_{2} where n_{1} and n_{2} are principal quantum numbers of the two states. Assuming Bohr’s model to be valid, the time period of the electron in the initial state is eight times that in the final state. The possible values of n_{1} and n_{2} are$ (1) $n_{1} = 6 and n_{2} = 2$ (2) $n_{1} = 8 and n_{2} = 1$ (3) $n_{1} = 8 and n_{2} = 2$ (4) $n_{1} = 4 and n_{2} = 2$ 291. $According to Bohr's theory, the moment of momentum of an electron revolving in 4^{th} orbit of hydrogen atom is:$ (1) $\frac{h}{π}$ (2) $\frac{h}{2 π}$ (3) $8 \frac{h}{π}$ (4) $2 \frac{h}{π}$ 292. $What is the wavelength of light for the least energetic photon emitted in the Lyman series of the hydrogen spectrum? (Take hc = 1240 eVnm)$ (1) $102 nm$ (2) $150 nm$ (3) $82 nm$ (4) $122 nm$ 293. $A particle of mass m moves in a circular orbit in a central potential field U (r) = \frac{1}{2} kr^{2} . If bohr's quantization conditions are applied, radii of possible orbitals and energy levels vary with quantum number n as :$ (1) $r_{n} \propto n, E_{n} \propto \frac{1}{n}$ (2) $r_{n} \propto n, E_{n} \propto n$ (3) $r_{n} \propto n^{2}, E_{n} \propto \frac{1}{n ^{2}}$ (4) $r_{n} \propto n, E_{n} \propto n$ 294. $Energy released when two deuterons (_{1} H^{2}) fuse to form a helium nucleus (_{2} He^{4}) is: (Given: Binding energy per nucleon of_{1} H^{2} = 1.1 MeV and binding energy per nucleon of_{2} He^{4} = 7.0 MeV)$ (1) $26.8 MeV$ (2) $8.1 MeV$ (3) $23.6 MeV$ (4) $5.9 MeV$ 295. $The energy released per fission of nucleus of 240X is 200 MeV. The energy released if all the atoms in 120g of pure 240X undergo fission is_____ x 1025 (Given N_{A} = 6x 1023)$ 296. $A monochromatic light is incident on a hydrogen sample in ground state. Hydrogen atoms absorb a fraction of light and subsequently emit radiation of six different wavelengths. The frequency of incident light is . The value of is (Given )$ 297. $A beam of electromagnetic radiation of intensity 6.4 \times 10^{- 5} W / cm^{2} is comprised of wavelength, ⋋ = 310 nm . It falls normally on a metal (work function = 2 eV) of surface area of 1 cm² . If one in 10³ photons ejects an electron, total number of electrons ejected in 1s is 10^{x} . (hc = 1240 eVnm, 1 eV = 1.6 \times 10^{- 19} J), then x is:$ 298. $The shortest wavelength of the spectral lines in the Lyman series of hydrogen spectrum is 915 A ˚ . The longest wavelength of spectral lines in the Balmer series will be____A ˚ .$ 299. $When a hydrogen atom going from n = 2 to n = 1 emits a photon, its recoil speed is \frac{x}{5} m / s . Where x = . (Use : mass of hydrogen atom = 1.6 \times 10^{- 27} kg)$ 300. $If three helium nuclei combine to form a carbon nucleus then the energy released in this reaction is______\times 10^{- 2} MeV . (Given 1 u = 931 MeV / c^{2}, atomic mass of helium = 4.002603 u)$