Atoms PYQs Set 11 (PDF)

Set 11 of 16 · Questions 301-330 of 453

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Mere Teacher · Previous Year Questions JEE Main Physics · Atoms · Set 11 (Q301-330)
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301. $Hydrogen atom from excited state comes to the ground state by emitting a photon of wavelength λ . If R is the Rydberg constant, the principal quantum number n of the excited state is$ (1) $\frac{λR}{λR - 1}$ (2) $\frac{λ}{λR - 1}$ (3) $\frac{λ R ^{2}}{λR - 1}$ (4) $\frac{λR}{λ - 1}$ 302. $A free electron of 2.6eV energy collides with H^{+} ion. This results in the formation of a hydrogen atom in the first excited state and a photon is released. Find the frequency of the emitted photon (h = 6.6 \times 1 0^{- 34} Js)$ (1) $1.45 \times 1 0^{16} MHz$ (2) $0.19 \times 1 0^{15} MHz$ (3) $1.45 \times 1 0^{9} MHz$ (4) $9.0 \times 1 0^{27} MHz$ 303. $Two sources of light emit X-rays of wavelength 1 nm and visible light of wavelength 500nm respectively. Both the sources emit light of the same power 200W. The ratio of the number density of photons of X -rays to the number density of photons of the visible light of the given wavelengths is:$ (1) $\frac{1}{250}$ (2) $\frac{1}{500}$ (3) $500$ (4) $250$ 304. $For wavelength of visible radiation of hydrogen spectrum Balmer gave an equation as λ = \frac{( km ^{2} )}{( m ^{2} - 4 )}, where ' m' is the integer value. The value of k in terms of Rydberg's constant R is$ (1) $\frac{4}{R}$ (2) $\frac{R}{4}$ (3) $4 R$ (4) $R$ 305. $For an electron moving in the n^{th} Bohr orbit the de-Broglie wavelength of an electron is$ (1) $nπr$ (2) $\frac{πr}{n}$ (3) $\frac{nr}{2 π}$ (4) $\frac{2 πr}{n}$ 306. $Find the radius of Be^{3 +} ions in its ground state assuming Bohr's model to be valid (a_{0} = 53 pm).$ (1) $20 pm$ (2) $18.2 pm$ (3) $16.2 pm$ (4) $13.2 pm$ 307. $Electron in hydrogen atom first jumps from third excited state to second excited state and then from second excited to the first excited state. The ratio of the wavelengths λ_{1} : λ_{2} emitted in the two cases is$ (1) $\frac{7}{5}$ (2) $\frac{27}{20}$ (3) $\frac{27}{5}$ (4) $\frac{20}{7}$ 308. $A hydrogen atom in is ground state absorbs 10.2 eV of energy. The angular momentum of electron of the hydrogen atom will increase by the value of: (Given, Plank's constant = 6.6 x 1 0^{- 34} Js)$ (1) $2.10 x 1 0^{- 34} Js$ (2) $1.05 x 1 0^{- 34} Js$ (3) $3.15 x 1 0^{- 34} Js$ (4) $4.2 x 1 0^{- 34} Js$ 309. $After absorbing a slowly moving neutron of Mass m_{N} (momentum \approx 0) a nucleus of mass M breaks into two nuclei of masses m_{1} and 5 m_{1} (6 m_{1} = M + m_{N}) respectively. If the de Broglie wavelength of the nucleus with mass m_{1} is λ, the de Broglie wevelength of the nucleus will be:$ (1) $5 λ$ (2) $λ /5$ (3) $λ$ (4) $25 λ$ 310. $Assuming the validity of Bohr's atomic model for hydrogen like ions the radius of Li^{++} ion in its ground state is given by \frac{1}{X} a_{0}, where X =_______ (Where a_{0} is the first Bohr's radius.)$ (1) $2$ (2) $9$ (3) $1$ (4) $3$ 311. $A 12. 5 eV electron beam is used to bombard gaseous hydrogen at room temperature. The number of spectral lines emitted will be:$ (1) $1$ (2) $4$ (3) $2$ (4) $3$ 312. $Electron in hydrogen atom first jumps from third excited state to second excited state and then from second excited to the first excited state. The ratio of the wavelength λ_{1} : λ_{2} emitted in the two cases is$ (1) $7/5$ (2) $27/20$ (3) $27/5$ (4) $20/7$ 313. $Match the following two columns. NEET 2024] Column I (Spectral lines of Hydrogen for transitions from) (A) n_{2} = 3 to n1=2 (B) n_{2} = 4 to n1=2 (C) n_{2} = 5 to n1=2 (D) n_{2} = 6 to n1=2 Column II (Wavelengths (nm)) (I) 410.2 (II) 434.1 (III) 656.3 (IV) 486.1 Choose the correct answer from the options given below.$ (1) $A-II, B-I, C-IV, D-III$ (2) $A-III, B-IV, C-II, D-I$ (3) $A-IV, B-III, C-I, D-II$ (4) $A-I, B-II, C-III, D-IV$ 314. $Total energy of electron in an excited state of hydrogen atom is - 3.4 eV . The kinetic and potential energy of electron in this state$ (1) $K = - 3.4 eV U=-6.8eV$ (2) $K = 3.4 eV U=-6.8eV$ (3) $K = - 6.8 eV U = + 3.4 eV$ (4) $K = + 10.2 eV U = - 13.6 eV$ 315. $Of the following pairs of species which one will have the same electronic configuration for both members?$ (1) $L i^{+} and N a^{+}$ (2) $He and N e^{+}$ (3) $H and Li$ (4) $C and N^{+}$ 316. $For which one of the following, Bohr model is not valid? [NEET 2020]$ (1) $Singly ionised helium atom (He^{+})$ (2) $Deuteron atom$ (3) $Singly ionised neon atom (Ne^{+})$ (4) $Hydrogen atom$ 317. $Given the value of Rydberg constant is 10^{7} m^{- 1}, the wave number of the last line of the Balmer series in hydrogen spectrum will be:$ (1) $2.5 \times 10^{7} m^{- 1}$ (2) $0.025 \times 10^{4} m^{- 1}$ (3) $0.5 \times 10^{7} m^{- 1}$ (4) $0.25 \times 10^{7} m^{- 1}$ 318. $Two radioactive elements A and B initially have same number of atoms. The half life of A is same as the average life of B. If λ_{A} and λ_{B} are decay constants of A and B respectively, then choose the correct relation from the given options.$ (1) $λ_{A} ln 2 = λ_{B}$ (2) $λ_{A} = λ_{B}$ (3) $λ_{A} = λ_{B} ln 2$ (4) $λ_{A} = 2 λ_{B}$ 319. $The period of revolution of an electron in the ground state of hydrogen atom is T . The period of revolution of the electron in the first excited state is$ (1) $2 T$ (2) $4 T$ (3) $6 T$ (4) $8 T$ 320. $If λ_{1} and λ_{2} are the wavelengths of the first nembers of the Lyman and Paschen series respectively, then λ_{1} : λ_{2} is$ (1) $1 : 3 q$ (2) $1 : 30$ (3) $7 : 50$ (4) $7 : 108$ 321. $An α -particle of energy 5 MeV is scattered through 180^{\circ} by gold nucleus. The distance of closest approach is of the order of$ (1) $10^{- 12} cm$ (2) $10^{- 16} cm$ (3) $10^{- 10} cm$ (4) $10^{- 14} cm$ 322. $Magnetic field at the centre of the hydrogen atom due to motion of electrons in n^{th} orbit is proportional to$ (1) $n^{4}$ (2) $n^{- 3}$ (3) $n^{3}$ (4) $n^{- 5}$ 323. $The energy equivalent of 1 g of substance is :$ (1) $5.6 \times 10^{12} MeV$ (2) $5.6 \times 10^{26} MeV$ (3) $11.2 \times 10^{24} MeV$ (4) $5.6 eV$ 324. $Let T_{1} and T_{2} be the energy of an electron in the first and second excited states of hydrogen atom, respectively. According to the Bohr's model of an atom, the ratio of T_{1} : T_{2} is [NEET 2022]$ (1) $4 : 1$ (2) $4 : 9$ (3) $9 : 4$ (4) $1 : 4$ 325. $Two radioactive materials A and B have decay constants 25 λ, and 16 λ respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of B to that of A will be "e" after a time \frac{1}{aλ} . The value of a is_______.$ 326. $In H-spectrum wavelength of 1st line of Balmer series is ⋋ = 6561Å . Find out -wavelength of 2nd line of same series in nm.$ 327. $A beam of monochromatic light is used to excite the electron in L i^{++} from the first orbit to the third orbit. The wavelength of monochromatic light is found to be x \times 1 0^{- 10} m. The value of x is______.[Given he = 1242 eV nml$ 328. $A light of energy 12,75 eV is incident on a hydrogen atom in its ground state. The atom absorbs the radiation and reaches to one of its excited states. The angular momentum of the atom in the excited state is \frac{x}{π} x 10-17eVs. The value of x is_________(use h = 4.14 x 10-15 eVs, c = 3 x 108 ms-1).$ 329. $An atom absorbs a photon of wavelength 500 nm and emits another photon of wavelength 600 nm . The net energy absorbed by the atom in this process is n \times 10^{- 4} eV . The value of n is [Assume the atom to be stationary during the absorption and emission process] (T ake h = 6.6 \times 10^{- 34} Js and c = 3 \times 10^{8} m s^{- 1}).$ 330. $A radioactive nucleus decays by two different process. The half life of the first process is 5 minutes and that of the second process is 30s. The effective half-life of the nucleus is calculated to be \frac{α}{11} s. The value of α is_______.$