CBSE Class 12 Physics HOTs Nuclei

Question. In a radioactive substance at t = 0, the number of atoms is 4 8×10 . Its half life period is 3 years. The number of atoms 1×10⁴ will remain after interval:
a. 9 yearss
b. 8 years
c. 6 years
d. 24 years
Answer : A

Question. During a negative beta decay:
a. An atomic electron is ejected
b. An electron which is already present within the nucleus is ejected
c. A neutron in the nucleus decays emitting an electron
d. A part of the binding energy is converted into electron
Answer : C

Question. What percentage of original radioactive atoms is left after five half lives:
a. 0.3%
b. 1%
c. 31%
d. 3.125%
Answer : D

Question. The half life of a radioactive element which has only 1/32 of its original mass left after a lapse of 60 days is:
a. 12 days
b. 32 days
c. 60 days
d. 64 days
Answer : A

Question. A radioactive nucleus undergoes a series of decay according to the scheme

If the mass number and atomic number of A are 180 and 72 respectively, then what are these number for A₄?
a. 172 and 69
b. 174 and 70
c.176 and 69
d.176 and 70
Answer : A

Question. The decay constant of radium is 4.28 x 10⁻⁴ per year. Its half life will be:
a. 2000 years
b. 1240 years
c. 63 years
d. 1620 years
Answer : D

Question. Atomic mass number of an element thorium is 232 and its atomic number is 90. The end product of this radioactive element is an isotope of lead (atomic mass 208 and atomic number 82). The number of alpha and beta particles emitted is:
a. α = 3, β = 3
b. α = 6, β = 4
c. α = 6, β = 0
d. α = 4, β = 6
Answer : B

Question. A radio-isotope has a half- life of 5 years. The fraction of the atoms of this material that would decay in 15 years
will be:
a. 1/8
b. 2/3
c. 7/8
d. 5/8
Answer : C

Question. Three α − particles and one β − particle decaying takes place in series from an isotope ₈₈Ra²³⁸. Finally the isotope obtained will be:
a.₈₄X²²⁰

b. ₈₆X²²²

c. ₈₃X²²⁴

d. ₈₃X²¹⁵
Answer : C

Question. Half life of Bi²¹⁰ is 5 days. If we start with 50,000 atoms of this isotope, the number of atoms left over after 10 days is:
a. 5,000
b. 25,000
c. 12,500
d. 20,000
Answer : C

Question. The radioactivity of a certain radioactive element drops to 1/64 of its initial value in 30 seconds. Its half life is:
a. 2 seconds
b. 4 seconds
c. 5 seconds
d. 6 seconds
Answer : C

Question. The half life of the isotope ₁₁Na²⁴ is 15 hrs. How much time does it take for 7/8^th of a sample of this isotope to decay?
a. 75 hrs
b. 65 hrs
c. 55 hrs
d. 45 hrs
Answer : D

Question. If 20 gm of a radioactive substance due to radioactive decay reduces to 10 gm in 4 minutes, then in what time 80 gm of the same substance will reduce to 10 gm?
a. In 8 minutes
b. In 12 minutes
c. In 16 minutes
d. In 20 minutes
Answer : B

Question. The count rate of a Geiger- Muller counter for the radiation of a radioactive material of half life of 30 minutes decreases to 5 s⁻¹ after 2 hours. The initial count rate was:
a.25 s⁻¹
b. 80 s⁻¹
c.625 s⁻¹
d. 20 s⁻¹
Answer : B

Question. A radioactive substance has a half life of 60 minutes. After 3 hours, the fraction of atom that have decayed would be:
a. 12.5%
b. 87.5%
c. 8.5%
d. 25.1%
Answer : B

Question. N atoms of a radioactive element emit n alpha particles per second. The half life of the element is: 
a. (n/N)sec
b.  (N/n)sec
c. (0.693 N/n)sec
d. (0.693 n/N)sec
Answer : C

Question. The average life T and the decay constant λ of a radioactive nucleus are related as:
a. Tλ =1
b. T = 0.693/T
c. T/λ = 1.
d. T = C/λ
Answer : 

Question. The half life of polonium is 140 days. After how many days, 16 gm polonium will be reduced to 1 gm (or 15g will decay)
a. 700 days
b. 280 days
c. 560 days
d. 420 days
Answer :C

Question. If Avogadro’s number is 6×10²³ then the number of protons, neutrons and electrons in 14g of ₆C¹⁴ are respectively:
a. 36×10²³ , 48×10²³ , 36×10²³
b. 36×10²³ , 36×10²³ , 36×10²¹
c. 48×10²³ , 36×10²³ , 48×10²¹
d. 48×10²³ , 48×10²³ , 36×10²¹
Answer : A

Question. Two Cu⁶⁴ nuclei touch each other. The electrostatics repulsive energy of the system will be:
a. 0.788 MeV
b. 7.88 MeV
c. 126.15 MeV
d. 788 MeV
Answer : C

Question. When ₉₂U²³⁵ undergoes fission. 0.1% of its original mass is changed into energy. How much energy is released if 1kg of ₉₂U²³⁵ undergoes fission:
a. 10 9×10¹⁰ J
b. 11 9×10¹¹ J
c. 12 9×10¹² J
d. 13 9×10¹³ J
Answer :D

Question. 1 g of hydrogen is converted into 0.993 g of helium in a thermonuclear reaction. The energy released is:
a. 63×10⁷ J
b. 63×10²⁰ J
c. 63×10¹⁴ J
d. 63×10²⁰ J
Answer : V

Question. The binding energy per nucleon of deuteron (²₁H) and helium nucleus (⁴₂He) is 1.1 MeV and 7 MeV respectively.
If two deuteron nuclei react to form a single helium nucleus, then the energy released is:
a. 13.9 MeV
b. 26.9 MeV
c. 23.6 MeV
d. 19.2 MeV
Answer : C

Question. The masses of neutron and proton are 1.0087 amu and 1.0073 amu respectively. If the neutrons and protons combine to form a helium nucleus (alpha particles) of mass 4.0015amu. The binding energy of the helium nucleus will be [1 amu= 931 MeV]
a. 28.4 MeV
b. 20.8 MeV
c. 27.3 MeV
d. 14.2 MeV
Answer : A

Question. A radioactive element emits 200 particles per second. After three hours 25 particles per second are emitted. The half life period of element will be:
a. 50 minutes
b. 60 minutes
c. 70 minutes
d. 80 minutes
Answer : B

Question. 1 mg gold undergoes decay with 2.7 days half-life period, amount left after 8.1 days is:
a. 0.91 mg
b. 0.25 mg
c. 0.5 mg
d. 0.125 mg
Answer : D

Question. In the nuclear fusion reaction ²₁H + ³₁H → ⁴₂He + n, given that the repulsive potential energy between the two nuclei is - 7.7x10^-14 J, the temperature at which the gases must be heated to initiate the reaction is nearly [Boltzmann’s constant k 1.38 10^-23 J/K]
a. 10⁹ K
b. 10⁷ K
c. 10⁶ K
d. 10³ K
Answer : A

Question. A nucleus with mass number 220 initially at rest emits an α-particle. If the Q value of the reaction is 5.5 MeV. Calculate the kinetic energy of the α-particle:
a. 4.4 MeV
b. 5.4 MeV
c. 5.6 MeV
d. 6.5 MeV
Answer : B

Question. Let m_p be the mass of a proton, m_n the mass of a neutron, M₁ the mass of a ²⁰₁₀Ne nucleus and M₂ the mass of a ⁴⁰₂₀Ca nucleus. Then:
a. M₂ = 2M₁
b. M₂ > 2M₁
c. M₂ < 2M₁
d. M₁ < (m_n + m_p)
Answer : C, D

Question. The ratio of radii of nuclei ²⁷₁₃Al and ¹²⁵₅₂Te is approximately:
a. 6 : 10
b. 13 : 52
c. 40 : 177
d. 14 : 7
Answer : A

Question. A radioactive substance decays to 1/16th of its initial activity in 40 days. The half-life of the radioactive substance expressed in days is:
a. 2.5
b. 5
c. 10
d. 20
Answer : C

Question. A heavy nucleus at rest breaks into two fragments which fly off with velocities in the ratio 8: 1. The ratio of radii of the fragments is
a. 1 : 2
b. 1 : 4
c. 4 : 1
d. 2 : 1
Answer : A

Question. A gamma ray photon creates an electron-positron pair. If the rest mass energy of an electron is 0.5 MeV and the total kinetic energy of the electron-positron pair is 0.78 MeV, then the energy of the gamma ray photon must be:
a. 0.78 MeV
b. 1.78 MeV
c. 1.28 MeV
d. 0.28 MeV
Answer : B

Question. What is the mass of one Curie of U²³⁴?
a. 3.7 × 10¹⁰ gm
b. 2.348 × 10²³ gm
c. 1.48 × 10^–11 gm
d. 6.25 × 10^–34 gm
Answer : C

Question. From a newly formed radioactive substance (Half-life 2 hours), the intensity of radiation is 64 times the permissible safe level. The minimum time after which work can be done safely from this source is:
a. 6 hours
b. 12 hours
c. 24 hours
d. 128 hours
Answer : B

Question. A atomic power reactor furnace can deliver 300 MW. The energy released due to fission of each of uranium atom U²³⁸ is 170 MeV. The number of uranium atoms fissioned per hour will be:
a. 5 × 10¹⁵
b. 10 × 10²⁰
c. 40 × 10²¹
d. 30 × 10²⁵
Answer : C

Question. The binding energy per nucleon is maximum in the case of:
a. ²₄He
b. ⁵⁶₂₆Fe
c. ¹⁴¹₅₆Ba
d. ²³⁵₉₂U
Answer : B

Question. The mass number of He is 4 and that for sulphur is 32.
The radius of sulphur nucleus is larger than that of helium, by times:
a. √8
b. 4
c. 2
d. 8
Answer : C

Question. Energy of 1g uranium is equal to:
a. 13 9.0×10¹³ J
b. 19 9.0×10¹⁹ J
c. 16 3.0×10¹⁶ J
d. 17 3.0×10¹⁷ J
Answer : A

Question. The energy equivalent of 1 kilogram of matter is about
a. 10⁻¹⁵ J
b. 1 J
c. 10⁻¹² J
d. 10¹⁷ J
Answer : D

Question. A sample of radioactive element has a mass of 10 gm at an instant t = 0. The approximate mass of this element in the sample after two mean lives is:
a. 2.50 gm
b. 3.70 gm
c. 6.30 gm
d. 1.35 gm
Answer : D

Question. The half-life of ²¹⁵ At is 100 μs. The time taken for the radioactivity of a sample of ²¹⁵ At to decay to 1/16^th of its initial value is:
a. 400 μs
b. 6.3 μs
c. 40 μs
d. 300 μs
Answer : A

Question. The mean lives of a radioactive substance for α and β emissions are 1620 years and 405 years respectively. After how much time will the activity be reduced to one fourth?
a. 405 year
b. 1620 year
c. 449 year
d. None of these
Answer : C

Question. At any instant the ratio of the amount of radioactive substances is 2: 1. If their half lives be respectively 12 and 16 hours, then after two days, what will be the ratio of the substances?
a. 1 : 1
b. 2 : 1
c. 1 : 2
d. 1 : 4
Answer : A

Question. If the binding energy of the deutrium is 2.23 MeV. The mass defect given in a.m.u. is :
a. – 0.0024
b. – 0.0012
c. 0.0012
d. 0.0024
Answer : D

Question. The binding energy per nucleon of deuterium and helium atom is 1.1 MeV and 7.0 MeV. If two deuterium nuclei fuse to form helium atom, the energy released is
a. 19.2 MeV
b. 23.6 MeV
c. 26.9 MeV
d. 13.9 MeV
Answer : B

Question. One microgram of matter converted into energy will give:
a. 90 J
b. 9×10³ J
c. 9×10¹⁰ J
d. 9×10⁵ J
Answer : C

Question. The binding energy per nucleon of O¹⁶ is 7.97 MeV and that of O¹⁷ is 7.75 MeV. The energy (in MeV) required to remove a neutron from O¹⁷ is:
a. 3.52
b. 3.64
c. 4.23
d. 7.86
Answer : C

Question. Binding energy per nucleon vs mass number curve for nuclei is shown in the figure. W, X, Y and Z are four nuclei indicated on the curve. The process that would release energy is:
a. Y → 2Z
b. W → X + Z
c. W → 2Y
d. X → Y + Z
Answer : C

Question. When ₉₀Th²²⁸ transforms to ₈₃Bi²¹², then the number of the emitted α − and β − particles is, respectively:
a. 8α , 7β
b. 4α ,7β
c. 4α ,4β
d. 4α ,1β
Answer : D

Question. Radius of ⁴₂He nucleus is 3 Fermi. The radius of ²⁰⁶₈₂Pb nucleus will be:
a.5 Fermi
b.6 Fermi
c.11.16 Fermi
d.8 Fermi
Answer : C

Question. Nuclear forces are:
a. Short ranged attractive and charge independent
b. Short ranged attractive and charge dependent
c. Long ranged repulsive and charge independent
d. Long ranged repulsive and charge dependent
Answer : A

Question. In helium nucleus, there are:
a. 2 protons and 2 electrons
b. 2 neutrons, 2 protons and 2 electrons
c. 2 protons and 2 neutrons
d. 2 positrons and 2 protons
Answer : C

Question. Atomic number of a nucleus is Z and atomic mass is M.
The number of neutron is:
a. M – Z
b. M
c. Z
d. M + Z
Answer : A

Question. If a proton and anti-proton come close to each other and annihilate, how much energy will be released:
a. 10 1.5 x 10⁻¹⁰ J
b. 10 3 x 10⁻¹⁰ J
c. 10 4.5 x 10⁻¹⁰ J
d.None of these
Answer : B

Question. The decay constant of a radioactive substance is 0.173 (years)–1 . Therefore:
a. nearly 63% of the radioactive substance will decay in (1/0.173) years
b. Half life of the radioactive substance is (1/0.173) year
c. one-fourth of the radioactive substance will be left after 8 years
d. all the above statements are true
Answer : A, C

Question. M_n and M_p represent mass of neutron and proton respectively. If an element having atomic mass M has Nneutron and Z-proton, then the correct relation will be:
a. M < NM_n + ZM_P
b. M > NM_n + ZM_P
c. M = NM_n + ZM_P
d. M = N M_n + M_P
Answer : A

Question. As compared ¹²C atom, ¹⁴C atom has:
a. Two extra protons and two extra electrons
b. Two extra protons but no extra electrons
c. Two extra neutrons and no extra electrons
d. Two extra neutrons and two extra electrons
Answer : C

Question. The mass defect in a particular nuclear reaction is 0.3 grams. The amount of energy liberated in kilowatt hours is (Velocity of light = 3 ×10⁸ m/s )
a. 1.5 ×10⁵
b. 2.5 ×10⁵
c. 3 ×10⁵
d. 7.5 ×10⁵
Answer : D

Question. On the bombardment of neutron with Boron. α-particle is emitted and product nuclei formed is:
a. ₆C¹²
b. ₃Li⁶
c. ₃Li⁷
d. ₄Be⁹
Answer : C

Question. The explosion of the atomic bomb takes place due to:
a. Nuclear fission
b. Nuclear fusion
c. Scattering
d. Thermionic emission
Answer : A

Question. For a nucleus to be stable, the correct relation between neutron number N and Proton number Z is:
a. N > Z
b. N = Z
c. N < Z
d. N ≥ Z
Answer : D

Question. Which of the following is the fusion reaction?
a. ₁H² + ₁H² → ₂He⁴
b. ₀n¹ + ₇N¹⁴ → ₆C¹⁴ + ₁H¹
c. ₀n¹ + ₉₂U²³⁸ → ₉₃Np²³⁹ + β^-1 − + γ
d. ₁H³ → ₂He³ + β^-1 + γ
Answer : A

Question. Thermal neutrons are those which:
a. Are at very high temperature
b. Move with high velocities
c. Have kinetic energies similar to those of surrounding molecules
d. Are at rest
Answer : C

Question. 200 MeV of energy may be obtained per fission of U²³⁵. A reactor is generating 1000 kW of power. The rate of nuclear fission in the reactor is:
a. 1000
b. 2×10⁸
c. 3.125×10¹⁶
d. 931
Answer : C