Bohr's Model & Hydrogen Spectrum — Practice Questions

Free NEET Physics multiple-choice questions on Bohr's Model & Hydrogen Spectrum. Attempt each question and reveal the answer with a full explanation.

If the radius of the ground state of a hydrogen atom is 0.53 Å , the radius of the first excited state of He + is: 1.06 Å 0.53 Å 0.265 Å 2.12 Å Which of the following quantities remains constant for an electron in a Bohr orbit of a hydrogen atom? Angular momentum Linear momentum Velocity Acceleration The ground state energy of a Li 2+ ion is: -122.4 eV -13.6 eV -54.4 eV -13.6 / 9 eV The shortest wavelength in the Paschen series of the hydrogen spectrum is approximately: 820 nm 91 nm 364 nm 121 nm The radius of the n th Bohr orbit of a hydrogen atom is r n . If the mass of the electron is doubled, the new radius of the n th orbit will be: r n / 2 2r n r n / 4 r n If the wavelength of the series limit of the Lyman series is L , then the wavelength of the series limit of the Pfund series is: 25L 16L 9L 5L The ratio of the de-Broglie wavelengths of an electron in the 1 st and 2 nd Bohr orbits of a hydrogen atom is: 1:2 2:1 1:4 4:1 The angular momentum of an electron in the n th orbit of Li 2+ ion is L . The angular momentum of the electron in the n th orbit of H -atom is: L 3L L/3 9L If the energy of the first Bohr orbit is -13.6 eV , what is the excitation energy required to move an electron from the ground state to the second excited state? 12.09 eV 10.2 eV 13.6 eV 1.89 eV According to the Bohr model, for an electron in a hydrogen-like atom, the frequency of revolution in the n th orbit is f n . The relation between f n and the principal quantum number n is: f n n -3 f n n -2 f n n 2 f n n 3 The ratio of the area of the orbit of the first excited state of a hydrogen atom to that of the ground state is: 16:1 4:1 2:1 8:1 The wavelength of the first line of the Paschen series in the hydrogen spectrum is approximately: 1875 nm 656 nm 121 nm 102 nm The energy level E n of a hydrogen atom is given by E n = -13.6/n 2 eV . The energy of the photon emitted in the transition from n=3 to n=1 is: 12.09 eV 10.2 eV 1.51 eV 13.6 eV Moseley's law for characteristic X-rays is expressed as = a(Z - b) . The constant b for K lines is approximately: 1 7.4 0 2 Which of the following transitions in a hydrogen atom results in the emission of a photon with the same wavelength as the n=4 to n=2 transition in He + ? n=2 to n=1 n=3 to n=2 n=4 to n=3 n=1 to n=2 The ratio of the speed of an electron in the ground state of hydrogen to that in the n=3 state of Li 2+ is: 1:1 1:3 3:1 1:9 The ratio of the magnetic moment of an electron in the n th Bohr orbit to its angular momentum is: e/(2m) e/m 2e/m m/e The wave number of the series limit (shortest wavelength) for the Lyman series in the hydrogen spectrum is R . What is the wave number of the series limit for the Balmer series? R/4 R/2 4R R/9 In a hydrogen atom, the electron makes a transition from n=n 1 to n=n 2 . The time period of revolution in the initial state is 8 times that in the final state. Possible values of n 1 and n 2 are: n 1=4, n 2=2 n 1=8, n 2=1 n 1=8, n 2=2 n 1=4, n 2=1 The force of attraction between the electron and the nucleus in a hydrogen atom is F . If the electron jumps from the n=1 to n=2 orbit, the new force of attraction is: F/16 F/4 F/2 F/8 If an electron in a hydrogen atom is replaced by a particle of the same charge but with mass 200 times that of the electron (a muon), the radius of the first Bohr orbit will: Decrease by a factor of 200 Increase by a factor of 200 Remain unchanged Decrease by a factor of 200 If 1 is the frequency of the series limit of the Lyman series, 2 is the frequency of the first line of the Lyman series, and 3 is the frequency of the series limit of the Balmer series, then which of the following relations is correct? 1 - u 2 = u 3 1 + u 2 = u 3 1 = u 2 - u 3 1 + u 3 = u 2 Using Moseley's Law, if the frequency of K X-ray of an element with Z=31 is f , what is the frequency for an element with Z=51 ? 25/9 f 5/3 f 1.5 f 4 f What is the maximum number of photons emitted when an electron in the n=4 state of a hydrogen atom returns to the ground state? 6 3 4 10 The speed of light c is related to the speed of an electron in the ground state of hydrogen v 1 by the fine structure constant . What is the approximate value of ? 1/137 1/2 1/1000 1/6.63 The energy of the photon emitted in the transition n=2 to n=1 in a He + ion is: 40.8 eV 10.2 eV 13.6 eV 54.4 eV The ratio of the wavelengths of the H line and the H line of the Balmer series in the hydrogen spectrum is: 27:20 20:27 5:3 3:5 If an electron in a hydrogen atom jumps from the 3 rd orbit to the 2 nd orbit, it emits a photon of wavelength . When it jumps from the 4 th orbit to the 3 rd orbit, the corresponding wavelength of the photon will be: 20 7 16 25 9 16 7 20 Which of the following transitions in a hydrogen atom emits the photon of the lowest frequency? n=10 n=9 n=2 n=1 n=3 n=2 n=4 n=3 The ratio of the de Broglie wavelength of an electron in the 2 nd orbit to that in the 4 th orbit of a hydrogen atom is: 1:2 2:1 1:4 4:1 In the Bohr model of the hydrogen atom, the ratio of the kinetic energy to the potential energy of the electron in any orbit is: -1/2 1/2 -2 2 The frequency of the series limit of the Balmer series is B . The frequency of the series limit of the Lyman series is L . The relation between them is: L = 4 B L = B L = 9 B B = 4 L An electron makes a transition from n=3 to n=1 in a hydrogen atom. The momentum of the emitted photon is: 8hR 9 hR 9 3hR 4 4hR 3 If the energy of the first Bohr orbit of a hydrogen atom is -E 0 , then the energy of the n=2 state of Li 2+ is: -2.25 E 0 -9 E 0 -4.5 E 0 -E 0 The potential energy of an electron in the second Bohr orbit of a hydrogen atom is: -6.8 eV -3.4 eV -13.6 eV -1.7 eV Calculate the ratio of the wavelength of the first line of the Lyman series to the series limit wavelength of the Lyman series in a hydrogen atom. 4/3 3/4 9/8 1/2 Which of the following transitions in a hydrogen atom emits a photon of the same wavelength as the transition from n=4 to n=2 in a He + ion? n=2 to n=1 n=3 to n=2 n=4 to n=3 n=3 to n=1 The ratio of the maximum wavelength to the minimum wavelength in the Balmer series of the hydrogen spectrum is: 9/5 5/9 4/3 3/4 In the Bohr model of the hydrogen atom, the orbital period of the electron in the n -th orbit is T n . The plot of 10 (T n/T 1) against 10 n will be a straight line with a slope of: 3 2 1.5 1 If the wavelength of the K X-ray of an element with atomic number Z=11 is , then the wavelength of the K X-ray of an element with atomic number Z=21 is: /4 /2 4 2 The ionization potential of the hydrogen atom is 13.6 V . What is the energy required to remove an electron from the n=2 state of the Li 2+ ion? 30.6 eV 13.6 eV 54.4 eV 122.4 eV The ratio of the area of the ground state orbit ( n=1 ) to the area of the first excited state orbit ( n=2 ) for a hydrogen atom is: 1/16 1/4 1/2 1/8 The wavelength of the first line of the Balmer series in hydrogen is 6563 . The wavelength of the first line of the Lyman series in hydrogen is approximately: 1215 1026 4861 912 The wavelength of the K X-ray line of an element with atomic number Z is approximately proportional to: (Z-1) -2 (Z-1) -1 (Z-7.4) -2 Z -2 The ratio of the longest wavelength in the Paschen series to the shortest wavelength in the Paschen series for a hydrogen atom is: 144/81 7/3 16/7 25/9 If the radius of the first Bohr orbit is 0.53 Å , the radius of the third Bohr orbit is: 4.77 Å 1.59 Å 2.12 Å 0.17 Å The orbital frequency of an electron in the ground state of a hydrogen atom is f . The frequency of the electron in the n=3 orbit is: f/27 f/3 f/9 3f The de Broglie wavelength of an electron in the n -th orbit of a hydrogen atom is n . Which of the following is correct? n ∝ n n ∝ n 2 n ∝ 1/n n ∝ n 3 The ratio of the wavelength of the second line of the Balmer series to the first line of the Balmer series in a hydrogen atom is: 20:27 27:20 3:4 4:9 The energy required to excite an electron from the n=2 to n=3 state in a He + ion is approximately: 7.56 eV 1.89 eV 13.6 eV 10.2 eV If the screen constant b in Moseley's law = a(Z-b) for K X-rays is 1, then the ratio of frequencies of K X-rays for Magnesium ( Z=12 ) and Titanium ( Z=22 ) is: 121:441 12:22 144:484 11:21 The wavelength of the first line of the Paschen series for a hydrogen atom is approximately: 1875 nm 656 nm 121 nm 1094 nm The angular speed of an electron in the n -th Bohr orbit of a hydrogen atom varies as: n -3 n -2 n -1 n -4 The radius of the ground state orbit of a hydrogen atom is 0.53 . The radius of the second orbit of a Li 2+ ion is: 0.707 0.353 1.06 0.53 Two radioactive substances A and B have decay constants 5 and respectively. At t = 0 they have the same number of nuclei. The ratio of number of nuclei of A to those of B will be (1/e) 2 after a time interval 4 2 1 2 1 4 The number of beta particles emitted by a radioactive substance is twice the number of alpha particles emitted by it. The resulting daughter is an : Isotope of parent Isobar of parent Isomer of parent Isotone of parent The energy of a photon emitted during the transition of an electron from n=3 to n=2 in a hydrogen atom is: 1.89 eV 1.51 eV 3.4 eV 10.2 eV The Binding energy per nucleon of 7 3Li and 4 2He nuclei are 5.60 , MeV and 7.06 , MeV , respectively. In the nuclear reaction 7 3Li + 1 1H -> 2 4 2He + Q , the value of energy Q released is :- 19.6 , MeV -2.4 , MeV 8.4 , MeV 17.3 , MeV A radio isotope 'X' with a half life 1.4 10 9 years decays to 'Y' which is stable. A sample of the rock from a cave was found to contain 'X' and 'Y' in the ratio 1:7 . The age of the rock is : 1.96 10 9 years 3.92 10 9 years 4.20 10 9 years 8.40 10 9 years 290 82 X Y e + Z - P e - Q In the nuclear emission stated above, the mass number and atomic number of the product Q respectively, are 280, 81 286, 80 288, 82 286, 81 Four statements are given ( A is mass number): A. The volume of a nucleus is proportional to A 1/3 . B. The volume of a nucleus is proportional to A . C. The difference in mass of an atom and its nucleus is called the mass defect. D. The difference in mass of a nucleus and its constituents is called the mass defect. Choose the correct answer from the options given below: A and D are true, but B and C are false B and D are true, but A and C are false B and C are true, but A and D are false A and C are true, but B and D are false An unknown nucleus has a nuclear density of 2.29 10 17 kg/m 3 and mass of 19.926 10 -27 kg . Its mass number A is approximately: (Take R 0 = 1.2 10 -15 m , 4 = 12.56 ) 16 20 12 19 The wavelength of the first line of Lyman series for hydrogen atom is equal to that of the second line of Balmer series for a hydrogen-like ion. The atomic number Z of the hydrogen-like ion is: 2 3 4 1 If the radius of the first Bohr orbit is r , then the de-Broglie wavelength of the electron in the third Bohr orbit is: 6 r 3 r 2 r 9 r The wavelength of the H line in Balmer series of hydrogen is 6563 . The wavelength of H line is: 4861 1215 8203 1025 When a hydrogen atom emits a photon during a transition from n=3 to n=1 , the recoil speed of the hydrogen atom (mass M ) is nearly: 8hR 9M 9hR 8M 3hR 4M hR M The Rydberg constant R is given by the expression: me 4 8 0 2 h 3 c me 4 4 0 2 h 3 c me 2 8 0 2 h 2 c m 2 e 4 8 0 2 h 3 c A hydrogen atom is excited from the ground state to an excited state with principal quantum number n=4 . The number of lines in the emission spectrum will be: 6 3 4 5 The ratio of the magnetic field at the center of a hydrogen atom due to the electron's motion in the first Bohr orbit to that in the second Bohr orbit is: 32 : 1 8 : 1 16 : 1 4 : 1 The velocity of an electron in the first excited state of a He + ion is ( c is the speed of light and is the fine structure constant): c c / 2 2 α c c / 4 For a hypothetical hydrogen-like atom, the potential energy is defined as U(r) = -k/r 2 . According to Bohr's quantization, the energy E n would be proportional to: n -4 n -2 n 2 n 4 When an electron jumps from n=2 to n=1 in a hydrogen atom, the recoil speed of the atom is approximately ( M is mass of hydrogen atom): 3hR/(4M) hR/M hR/(2M) 3hR/(2M) The energy levels of a certain hypothetical atom are given by E n = -A/n 2 . If the wavelength of the photon emitted in the transition n=3 to n=2 is , then the wavelength for n=4 to n=2 is: 27 /32 32 /27 9 /16 16 /9 When a hydrogen atom emits a photon corresponding to the transition n=3 to n=1 , the recoil momentum of the atom is (where h is Planck's constant and R is Rydberg constant): 8hR/9 hR/9 9hR/8 3hR/4 If the electron in a hydrogen atom jumps from the n=3 orbit to the n=2 orbit, the frequency of the emitted radiation is u . What is the frequency of radiation emitted when it jumps from n=4 to n=2 ? 27 20 u 20 27 u 9 16 u 16 9 u According to the Bohr correspondence principle, for very large values of the principal quantum number n , the frequency of radiation emitted during a transition from n to n-1 is proportional to: n -3 n -2 n -1 n -4 The centripetal acceleration of an electron in the n -th Bohr orbit of a hydrogen atom is proportional to: n -4 n -2 n -3 n -1 If the wavelength of K radiation of an element of atomic number Z=41 is , then the atomic number of an element whose K radiation has a wavelength 4 is: 21 11 81 31 According to Bohr's model, the velocity of an electron in the n -th orbit ( v n ) and the principal quantum number n are related as: v n ∝ 1/n v n ∝ n v n ∝ 1/n 2 v n ∝ n 2 A nuclide of an alkaline earth metal undergoes radioactive decay by emission of the α-particles in succession. The group of the periodic table to which the resulting daughter element would belong is :- Gr. 4 Gr.6 Gr.16 Gr.14 Consider that an electron is revolving in an excited state of Hydrogen atom with velocity 25.6 10 5 ms -1 . The radius of the orbit is x 10 -9 m. The value of x is: [Take the mass of electron to be 9 10 -31 kg, charge of electron =-1.6 10 -19 C and 1 4 0 =9 10 9 Nm 2 C -2 ] 4 3 2 1 If the wavelength of the series limit of the Lyman series for a hydrogen atom is L , then the wavelength of the series limit of the Balmer series is: 4 L 9 L 2 L L / 4 What is the maximum number of spectral lines emitted when an electron in a hydrogen atom jumps from the n=5 state to the n=2 state? 6 10 3 15 What is the maximum number of spectral lines possible when an electron in the 4 th excited state of a hydrogen atom returns to the ground state? 10 6 15 4 The kinetic energy of an electron in the n -th Bohr orbit is K , and its potential energy is U . Which of the following is correct? U = -2K U = -K U = K/2 U = 2K The energy of an electron in the ground state of a hydrogen atom is -13.6 eV . If the electron is in the n=4 state, the amount of energy required to ionize the atom is: 0.85 eV 13.6 eV 3.4 eV 1.51 eV In a hydrogen atom, if the electron moves from the n=3 to the n=2 orbit, the ratio of the initial and final angular momentum is: 3:2 9:4 2:3 4:9 Which transition in a hydrogen atom corresponds to the shortest wavelength emission? n=5 n=1 n=2 n=1 n=4 n=2 n=5 n=4 What is the ratio of the frequency of the first line of the Lyman series to that of the series limit of the Lyman series? 3:4 1:4 4:3 1:2 The ionization energy of hydrogen atom is 13.6 eV . The ionization energy of He + ion is: 54.4 eV 27.2 eV 13.6 eV 6.8 eV How many spectral lines are emitted when an electron jumps from n=5 to n=1 in a hydrogen atom? 10 5 15 4 In a Bohr atom, the ratio of the speed of an electron in the n=1 orbit to that in the n=3 orbit is: 3:1 1:3 9:1 1:9 If an electron drops from n=4 to n=2 in a hydrogen atom, the series of the spectral line belongs to: Balmer series Lyman series Paschen series Brackett series The Bohr model of atoms is not applicable to: Neutral Helium atom Singly ionized Helium Doubly ionized Lithium Hydrogen atom The frequency of revolution of an electron in the ground state of a hydrogen atom is f . What is the frequency of revolution of the electron in the first excited state ( n=2 )? f/8 f/4 f/2 f/16 The total energy of an electron in the ground state of a hydrogen atom is -13.6 eV . The kinetic energy of an electron in the first excited state is: 3.4 eV 6.8 eV 13.6 eV 1.51 eV The energy of a photon of wavelength 400 nm is approximately: 3.1 eV 1.5 eV 4.2 eV 2.1 eV The energy required to remove an electron from the n=2 state to n = in a hydrogen atom is: 3.4 eV 13.6 eV 1.51 eV 10.2 eV According to Bohr's principle, the relation between principle quantum number n and radius of orbit r is: r n 2 r n r 1/n r 1/n 2 According to Bohr's model, the quantization of angular momentum for an electron in a hydrogen atom is a direct consequence of: The wave nature of the electron forming standing waves The particle nature of the electron The conservation of energy The Pauli exclusion principle In a hydrogen atom, the ratio of the potential energy to the kinetic energy of the electron in any Bohr orbit is: -2 2 -1 1 Bohr's second postulate regarding the quantization of angular momentum states that L = n . Here is equal to: h / 2 h / π 2π h h / 4π The frequency of the first line of the Lyman series in a hydrogen atom is . What is the frequency of the corresponding line in a He + ion? 4 2 /4 The ratio of the longest wavelength in the Lyman series to the shortest wavelength in the Lyman series is: 4/3 9/8 3/4 2/1 According to Bohr's theory, the angular momentum of an electron in the 4 th orbit is: 2h 4h h 3h 2 If the radius of the ground state orbit of a hydrogen atom is 0.53 , what is the radius of the n=2 orbit of a Li 2+ ion? 0.707 0.35 1.06 2.12 The time period of revolution of an electron in the n th orbit of a hydrogen atom is T . The time period in the 2 nd orbit compared to the 1 st orbit is: 8T 4T 2T 16T What is the energy of a photon emitted when an electron in a hydrogen atom jumps from n=4 to n=3 ? 0.66 eV 0.85 eV 1.51 eV 10.2 eV The wave number of the last line of the Balmer series in the hydrogen spectrum is: R/4 R R/9 4/R What is the ratio of the speed of an electron in the ground state of hydrogen ( Z=1 ) to the speed of an electron in the ground state of Li 2+ ( Z=3 )? 1:3 3:1 1:9 1:1 Which of the following transitions results in the emission of a photon with the longest wavelength in the Balmer series? n=3 n=2 n=4 n=2 n=5 n=2 n= n=2 The radius of the innermost electron orbit of a hydrogen atom is 5.3 10 -11 m . What is the radius of the n=3 orbit? 4.77 10 -10 m 1.59 10 -10 m 1.06 10 -10 m 2.12 10 -10 m Which of the following spectral series of the hydrogen atom lies entirely in the ultraviolet region? Lyman series Balmer series Paschen series Brackett series What is the orbital speed of an electron in the second orbit of a Li 2+ ion? (Given: speed of electron in the ground state of H-atom is v ) 1.5 v 3 v 0.67 v v The minimum wavelength of X-rays produced by an electron accelerated through a potential difference of V volts is: hc/eV eV/hc hcV/e e/hcV The ratio of the energy of the first excited state of a hydrogen atom to that of a He + ion in the same state is: 1:4 1:2 4:1 1:1 The ratio of the speed of an electron in the ground state of a hydrogen atom ( Z=1 ) to the speed of light ( c ) is approximately: 1/137 1/237 1/337 1/437 What is the ground state radius of a Be 3+ ion? (Take a 0 as the Bohr radius for hydrogen) 0.25 a 0 4 a 0 0.5 a 0 2 a 0 The wave number of the series limit of the Lyman series for a Li 2+ ion is ( R is Rydberg constant): 9 R R 4 R 3 R In Bohr's model of the hydrogen atom, the potential energy of the electron in an orbit of radius r is: -e 2 / (4 0 r) e 2 / (4 0 r) -e 2 / (8 0 r) e 2 / (8 0 r) The diameter of the first Bohr orbit of a hydrogen atom is approximately: 1.06 Å 0.53 Å 2.12 Å 0.26 Å The de Broglie wavelength of an electron in the n=4 Bohr orbit is given by . The circumference of this orbit is: 4 / 4 16 2 If the radius of the n th Bohr orbit of a hydrogen atom is r n , then the radius of the n th orbit of a Li 2+ ion is: r n/3 3r n r n/9 9r n The energy of the ground state of a hydrogen-like ion is -54.4 eV . The ion is: He + Li 2+ Be 3+ H If the wavelength of the first line of the Lyman series is , the Rydberg constant R is: 4/(3 ) 3/(4 ) /3 3 /4 In the reaction 2 1 H + 3 1 H 4 2 He + 1 0 n . If the binding energies of 2 1 H , 3 1 H and 4 2 He are respectively a , b and c (in MeV), then the energy (in MeV) released in this reaction is a+b+c c+a-b c-a-b a+b-c The nuclei of which one of the following pairs of nuclei are isotones : 34 Se 74 , 31 Ga 71 38 Sr 84 , 38 Sr 86 42 Mo 92 , 40 Zr 92 20 Ca 40 , 16 S 32 The energy of an electron in the ground state of a hydrogen atom is -13.6 eV . The energy of the photon emitted when an electron jumps from n=4 to n=2 is: 2.55 eV 3.40 eV 0.85 eV 10.2 eV In any fission process the ratio mass of fission products mass of parent nucleus is- Greater than 1 Depends on the mass of the parent nucleus Equal to 1 Less than 1 Fission of nuclei is possible because the binding energy per nucleon in them- Decreases with mass number at low mass numbers Increases with mass number at low mass numbers Decreases with mass number at high mass numbers Increases with mass number at high mass numbers The binding energy of deuteron is 2.2 MeV and that of 4 2He is 28MeV. If two deuterons are fused to form one 4 2He then the energy released is:- 25.8 MeV 23.6 MeV 19.2 MeV 30.2 MeV In a radioactive material the activity at time t 1 is R 1 and at a later time t 2 , it is R 2 . If the decay constant of the material is , then R 1 = R 2 e - (t 1-t 2) R 1 = R 2 e (t 1-t 2) R 1 = R 2 (t 2/t 1) R 1 = R 2 The radius of Germanium (Ge) nuclide is measured to be twice the radius of 9 4Be . The number of nucleons in Ge are:- 73 74 75 72 In a radioactive decay process, the negatively charged emitted -particles are the electrons produced as a result of the decay of neutrons inside the nucleus the electrons produced as a result of collisions between atoms the electrons orbiting around the nucleus the electrons present inside the nucleus. A nucleus A Z X has mass represented by M(A, Z). If M p and M n denote the mass of proton and neutron respectively and B.E. the binding energy in MeV, then B.E. = [ZM p + (A-Z)M n - M(A, Z)]c 2 B.E. = [ZM p + ZM n - M(A, Z)]c 2 B.E. = M(A, Z) - ZM p - (A-Z)M n B.E. = [M(A, Z) - ZM p - (A-Z)M n]c 2 If the nucleus 27 13 Al has nuclear radius of about 3.6 fm, then 125 32 Te would have its radius approximately as 9.6fm 12.0fm 4.8fm 6.0fm. In the nuclear decay given below : A Z X A Z+1 Y A-4 Z-1 B A-4 Z-1 B The particles emitted in the sequence are : , , , , , , , , The half life of a radioactive isotope ‘X’ is 20 years. It decays to another element ‘Y’ which is stable. The two elements ‘X’ and ‘Y’ were found to be in the ratio 1 : 7 in a sample of a given rock. The age of the rock is estimated to be 40 years 60 years 80 years 100 years An electron of mass m and charge e is accelerated from rest through a potential difference V and strikes a target. The maximum frequency of the X-rays produced is: eV/h h/eV eV/mc 2 mc 2/h A certain mass of Hydrogen is changed to Helium by the process of fusion. The mass defect in fusion reaction is 0.02866 u. The energy liberated per u is (given 1 u = 931 MeV) 2.67 MeV 26.7 MeV 6.675 MeV 13.35 MeV When an -particle of mass 'm' moving with velocity 'v' bombards on a heavy nucleus of charge 'Ze', its distance of closest approach from the nucleus depends on m as : 1 m 1 m 1 m 2 m The energy liberated per nuclear fission is 200 MeV. If 10 20 fissions occur per second the amount of power produced will be 2 10 22 W 32 10 8 W 16 10 8 W 5 10 11 W For a radioactive material, half-life is 10 minutes. If initially there are 600 number of nuclei, the time taken (in minutes) for the disintegration of 450 nuclei is 30 10 20 15 α-particle consists of : 2 protons only 2 protons and 2 neutrons only 2 electrons, 2 protons and 2 neutrons 2 electrons and 4 protons only The energy equivalent of 0.5 g of a substance is : 4.5 10 13 J 1.5 10 13 J 0.5 10 13 J 4.5 10 16 J When a uranium isotope 235 92 U is bombarded with a neutron, it generates 89 36 Kr , three neutrons and : 91 40 Zr 101 36 Kr 103 36 Kr 144 56 Ba A nucleus with mass number 240 breaks into two fragments each of mass number 120, the binding energy per nucleon of unfragmented nuclei is 7.6 MeV while that of fragments is 8.5 MeV. The total gain in the Binding Energy in the process is 9.4 MeV 804 MeV 216 MeV 0.9 MeV The half-life of a radioactive nuclide is 100 hours. The fraction of original activity that will remain after 150 hours would be 1 2 2 2 3 2 3 2 1 2 A radioactive nucleus A Z X undergoes spontaneous decay in the sequence A Z X Z-1 B Z-3 C Z-2 D , where Z is the atomic number of element X . The possible decay particles in the sequence are , + , - + , , - - , , + , - , + What is the radius of the n=2 orbit of a He + ion if the Bohr radius of a hydrogen atom is a 0 ? a 0 a 0 2 2a 0 4a 0 Tritium, a radioactive isotope of hydrogen, emits which of the following particles? Alpha (α) Gamma (γ) Neutron (n) Beta (β - ) In the given nuclear reaction, the element X is 22 11 Na X + e + + 23 10 Ne 22 10 Ne 22 12 Mg 23 11 Na A nucleus of mass number 189 splits into two nuclei having mass number 125 and 64. The ratio of radius of two daughter nuclei respectively is 4 : 5 5 : 4 25 : 16 1 : 1 The half life of a radioactive substance is 20 minutes. In how much time, the activity of substance drops to ( 1 16 ) th of its initial value? 20 minutes 40 minutes 60 minutes 80 minutes In the Bohr model of a hydrogen atom, the centripetal force is furnished by the Coulomb attraction between the proton and the electron. If a 0 is the radius of the ground state orbit, m is the mass and e is the charge of an electron, and 0 is the vacuum permittivity, the speed of the electron is: e 4 0 a 0 m e 0 a 0 m 4 0 a 0 m e 4 0 a 0 m e Which of the following transitions in a hydrogen atom emits the photon of highest frequency? n=2 n=1 n=1 n=2 n=6 n=2 n=2 n=6 When a hydrogen atom is raised from the ground state to an excited state: P.E. increases and K.E. decreases P.E. decreases and K.E. increases Both P.E. and K.E. increase Both P.E. and K.E. decrease The de-Broglie wavelength of an electron in the ground state of the hydrogen atom is ( a 0 is Bohr radius): 2 a 0 a 0 a 0 4 a 0 The ratio of the speed of the electron in the first Bohr orbit of hydrogen and the speed of light is nearly: 1/137 1/237 1/100 1/10 The ratio of the wavelengths of the longest wavelength lines in the Lyman and Balmer series of hydrogen spectrum is: 5/27 3/23 9/31 7/29 Which of the following transitions in a hydrogen atom emits a photon of the shortest wavelength? n=2 n=1 n=4 n=3 n=3 n=2 n=5 n=4 The shortest wavelength in the Lyman series of hydrogen spectrum is 912 . The shortest wavelength in the Balmer series is: 3648 1824 912 2736 The total energy of an electron in the first excited state of a hydrogen atom is -3.4 eV . Its potential energy in this state is: -6.8 eV 6.8 eV -3.4 eV 3.4 eV The ratio of the kinetic energy to the total energy of an electron in a Bohr orbit is: -1 1 2 -2 The ratio of the magnetic dipole moment of an electron revolving in the ground state of a hydrogen atom to its angular momentum is: e 2m e m 2e m e 2π m The ratio of the frequency of revolution of an electron in the second Bohr orbit to that in the third Bohr orbit of a hydrogen atom is: 27 : 8 8 : 27 4 : 9 9 : 4 The area enclosed by the electron orbit in a hydrogen atom is A n . The variation of (A n / A 1) with (n) is a straight line with a slope of: 4 2 3 1 The ratio of the wavelength of the H line of the Balmer series for hydrogen to that of the H line for He + is: 4 : 1 1 : 4 2 : 1 1 : 2 If the radius of the ground state orbit of a hydrogen atom is a 0 , then the radius of the first excited state of a He + ion is: 2a 0 a 0 4a 0 a 0 / 2 In the ground state of a hydrogen atom, the electron revolves in a circular orbit of radius 0.53 Å with a speed of 2.2 10 6 m/s . The equivalent current is approximately: 1.06 mA 1.06 A 6.6 mA 2.2 mA The ratio of the wavelengths of the first line of the Lyman series to the first line of the Balmer series in a hydrogen atom is: 5 : 27 27 : 5 1 : 4 4 : 9