Nuclei PYQs

In the first excited state of hydrogen atom, the energy of its electron is −3.4 eV. The radial distance of the electron from the hydrogen nucleus in this case is approximately: (Take 1 eV = 1.6 × 10⁻¹⁹ J, e = 1.6 × 10⁻¹⁹ C and 1/4πε₀ = 9 × 10⁹ N m²/C²)

Four statements are given (A is mass number): A. The volume of a nucleus is proportional to A¹ᐟ³. 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:

An unknown nucleus has a nuclear density of 2.29 × 10¹⁷ kg/m³ and mass of 19.926 × 10⁻²⁷ kg. Its mass number A is approximately: (Take R₀ = 1.2 × 10⁻¹⁵ m, 4π = 12.56)

In the nuclear emission stated above, the mass number and atomic number of the product Q respectively, are:

The half life of a radioactive substance is 20 minutes. In how much time, the activity of the substance drops to (1/16)th of its initial value?

In the given nuclear reaction, the element X is: ²²₁₁Na → X + e⁺ + ν

A nucleus of mass number 189 splits into two nuclei having mass numbers 125 and 64. The ratio of radius of two daughter nuclei respectively is:

A radioactive nucleus $^{A}_{Z}X$ undergoes spontaneous decay in the sequence: where Z is the atomic number of element X The possible decay particles in the sequence are:

The half-life of a radioactive nuclide is 100 hours. The fraction of original radioactivity that will remain after 150 hours would be:

A nucleus with mass number $240$ breaks into two fragments each of mass number $120$. The binding energy per nucleon of the unfragmented nucleus is $7.6\,\text{MeV}$, while that of each fragment is $8.5\,\text{MeV}$. The total gain in binding energy in the process is:

The energy equivalent of 0.5 g of a substance is :

When a uranium isotope $^{235}_{92}\text{U}$ is bombarded with a neutron, it generates $^{89}_{36}\text{Kr}$, three neutrons and:

The rate of radioactive disintegration at an instant for a radioactive sample of half-life $2.2 \times 10^9\ \text{s}$ is $10^{10}\ \text{s}^{-1}$. The number of radioactive atoms in the sample at that instant is:

For a radioactive material, half-life is 10 minutes. If initially there are 600 number of nuclei, the time taken (in minutes) for disintegration of 450 nuclei is:

Radioactive material $A$ has decay constant $8\lambda$ and material $B$ has decay constant $\lambda$. Initially they have the same number of nuclei. After what time will the ratio of number of nuclei of material $B$ to that of material $A$ be $\dfrac{1}{e}$?

The half-life of a radioactive substance is $30$ minutes. The time (in minutes) taken between $40\%$ decay and $85\%$ decay of the same radioactive substance is:

A nucleus of uranium decays at rest into nuclei of thorium and helium. Then:

The binding energy per nucleon of ⁷₃Li and ⁴₂He nuclei are 5.60 MeV and 7.06 MeV, respectively. In the nuclear reaction ⁷₃Li + ¹₁H → ⁴₂He + Q, the value of energy Q released is:

A radio isotope X with a half-life 1.4 × 10⁹ 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:

What is the maximum number of orbitals that can be identified with the following quantum numbers? n = 3, ℓ = 1, m$_ℓ$ = 0

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

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 $1\,u = 931\,\text{MeV}$)

The half life of a radioactive nucleus is 50 days. The time interval $(t_2-t_1)$ between the time $t_2$ when $\dfrac{2}{3}$ of it has decayed and the time $t_1$ when $\dfrac{1}{3}$ of it has decayed is:

Two radioactive nuclei P and Q, in a given sample decay into a stable nucleus R. At time t = 0, number of P species are 4N₀ and that of Q are N₀. Half-life of P (for conversion to R) is 1 minute whereas that of Q is 2 minutes. Initially there are no nuclei of R present in the sample. When number of nuclei of P and Q are equal, the number of nuclei of R present in the sample will be:

The decay constant of a radioisotope is $\lambda$. If $A_1$ and $A_2$ are its activities at times $t_1$ and $t_2$ respectively, the number of nuclei which have decayed during the time interval $(t_1 - t_2)$ is

The binding energy per nucleon in deuterium and helium nuclei are 1.1 MeV and 7.0 MeV, respectively. When two deuterium nuclei fuse to form a helium nucleus the energy released in the fusion is

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:

In a Rutherford scattering experiment when a projectile of charge $Z_1$ and mass $M_1$ approaches a target nucleus of charge $Z_2$ and mass $M_2$, the distance of closest approach is $r_0$. The energy of the projectile is:

In the nuclear decay given below: $$^{A}_{Z}X \rightarrow {}^{A}_{Z+1}Y \rightarrow {}^{A-4}_{Z-1}B^{*} \rightarrow {}^{A-4}_{Z-1}B$$ The particles emitted in the sequence are:

Two radioactive materials X₁ and X₂ have decay constants 5λ and λ respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of X₁ to that of X₂ will be 1/e after a time

Two nuclei have their mass numbers in the ratio 1 : 3. The ratio of their nuclear densities would be

If M(A; Z), Mₚ and Mₙ denote the masses of the nucleus A/Z X, proton and neutron respectively in units of u (1 u = 931.5 MeV/C²) and BE represents its binding energy in MeV, then

Which of the following is a correct difference between nuclear force and Coulomb force?

The binding energy of deuteron is 2.2 MeV and that of ⁴₂He is 28 MeV. If two deuterons are fused to form one ⁴₂He then the energy released is:

In a radioactive material the activity at time t₁ is R₁ and at a later time t₂, it is R₂. If the decay constant of the material is λ, then:

The radius of germanium (Ge) nucleus is measured to be twice the radius of ⁹₄Be. The number of nucleons in Ge are:

In the reaction $^2_1H + ^3_1H \rightarrow ^4_2He + ^1_0n$, if the binding energies of $^2_1H$, $^3_1H$ and $^4_2He$ are respectively $a$, $b$ and $c$ (in MeV), then the energy released in this reaction is:

The nuclei of which one of the following pairs of nuclides are isotones?

Fission of nuclei is possible because the binding energy per nucleon in them:

In any fission process the ratio (mass of fission products/mass of parent nucleus) is :