Atoms And 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)

A particle of mass $m$ is moving around the origin with a constant force $F$ pulling it towards the origin. If Bohr model is used to describe its motion, the radius $r$ of the $n^{th}$ orbit and the particle’s speed $v$ in the orbit depend on $n$ as

Energy and radius of first Bohr orbit of $\mathrm{He}^+$ and $\mathrm{Li}^{2+}$ are given.

Match List I with List II. Choose the correct answer from the options given below:

Given below are two statements: Statement I: Atoms are electrically neutral as they contain equal number of positive and negative charges. Statement II: Atoms of each element are stable and emit their characteristic spectrum. In the light of the above statements, choose the most appropriate answer from the options given below:

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 hydrogen spectrum, the shortest wavelength in the Balmer series is λ. The shortest wavelength in the Brackett series is :

The radius of inner most orbit of hydrogen atom is 5.3 × 10⁻¹¹ m. What is the radius of third allowed orbit of hydrogen atom?

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

Let T₁ and T₂ be the energy of an electron in the first and second excited states of hydrogen atoms, respectively. According to Bohr's model of an atom, the ratio T₁ : T₂ is:

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:

If radius of second Bohr orbit of the He+ ion is 105.8 pm, what is the radius of third Bohr orbit of of third Bohr orbit of Li²⁺ ion?

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:

For which one of the following, Bohr model is not valid?

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 radius of the first permitted Bohr orbit, for the electron, in a hydrogen atom equals 0.51 Å and its ground state energy equals -13.6 eV. If the electron in the hydrogen atom is replaced by muon (μ⁻) [charge same as electron and mass 207 mₑ], the first Bohr radius and ground state energy will be,

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:

The ratio of kinetic energy to the total energy of an electron in a Bohr orbit of the hydrogen atom, is:

The ratio of wavelengths of the last line of Balmer series and the last line of Lyman series 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 $\dfrac{1}{e}$?

If an electron in a hydrogen atom jumps from the 3rd orbit to the 2nd orbit, it emits a photon of wavelength $\lambda$. When it jumps from the 4th orbit to the 3rd orbit, the corresponding wavelength of the photon will be:

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:

In the spectrum of hydrogen, the ratio of the longest wavelength in the Lyman series to the longest wavelength in the Balmer series is:

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

Hydrogen atom in ground state is excited by a monochromatic radiation of λ = 975 Å. Number of spectral lines in the resulting spectrum emitted will be:

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 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:

Out of the following which one is not a possible energy for a photon to be emitted by hydrogen atom according to Bohr's atomic model?

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 electron in the hydrogen atom jumps from excited state (n = 3) to its ground state (n = 1) and the photons thus emitted irradiate a photosensitive material. If the work function of the material is 5.1 eV, the stopping potential is estimated to be (the energy of the electron in nth state Eₙ = −(13.6 / n² eV))

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:

The ionization energy of the electron in hydrogen atom in its ground state is $13.6\,\text{eV}$. The atoms are excited to higher energy levels to emit radiations of 6 wavelengths. Maximum wavelength corresponds to transition between:

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:

The ground state energy of hydrogen atom is -13.6 eV. When its electron is in the first excited state, its excitation energy is

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

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:

Ionization potential of hydrogen atom is 13.6 eV. Hydrogen atoms in the ground state are excited by monochromatic radiation of photon energy 12.1 eV. According to Bohr's theory, the spectral lines emitted by hydrogen will be:

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:

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 :