An atom ${ }_3^8 X$ is bombarded by shower of fundamental particles and in 10 s this atom absorbed 10 electrons, 10 protons and 9 neutrons. The percentage growth in the surface area of the nucleons is recorded by :

The binding energy for the following nuclear reactions are expressed in MeV .

$ \begin{aligned} & { }_2 \mathrm{He}^3+{ }_0 \mathrm{n}^1 \rightarrow{ }_2 \mathrm{He}^4+20 \mathrm{MeV} \\ & { }_2 \mathrm{He}^4+{ }_0 \mathrm{n}^1 \rightarrow{ }_2 \mathrm{He}^5-0.9 \mathrm{MeV} \end{aligned} $

If $\mathrm{X}_3, \mathrm{X}_4, \mathrm{X}_5$ denote the stability of ${ }_2 \mathrm{He}^3,{ }_2 \mathrm{He}^4$ and ${ }_2 \mathrm{He}^5$, respectively, then the correct order is :

Two electrons are moving in orbits of two hydrogen like atoms with speeds $3 \times 10^5 \mathrm{~m} / \mathrm{s}$ and $2.5 \times 10^5 \mathrm{~m} / \mathrm{s}$ respectively. If the radii of these orbits are nearly same then the possible order of energy states are $\_\_\_\_$ respectively.

Given below are two statements :

Statement I : For all elements, greater the mass of the nucleus, greater is the binding energy per nucleon.

Statement II : For all elements, nuclei with less binding energy per nucleon transforms to nuclei with greater binding energy per nucleon.

In the light of the above statements, choose the correct answer from the options given below

Which of the following pair of nuclei are isobars of the element?

In hydrogen atom spectrum, ( $R \rightarrow$ Rydberg's constant)

A. the maximum wavelength of the radiation of Lyman series is $\frac{4}{3 R}$

B. the Balmer series lies in the visible region of the spectrum

C. the minimum wavelength of the radiation of Paschen series is $\frac{9}{R}$

D. the minimum wavelength of Lyman series is $\frac{5}{4 R}$

Choose the correct answer from the options given below :

The smallest wavelength of Lyman series is 91 nm . The difference between the largest wavelengths of Paschen and Balmer series is nearly $\_\_\_\_$ nm.

The minimum frequency of photon required to break a particle of mass 15.348 amu into $4 \alpha$ particles is $\_\_\_\_$ kHz .

[mass of He nucleus = $4.002 \mathrm{amu}, 1 \mathrm{amu}=1.66 \times 10^{-27} \mathrm{~kg}, \mathrm{~h}=6.6 \times 10^{-34} \mathrm{~J} . \mathrm{s}$ and $\mathrm{c}=3 \times 10^8 \mathrm{~m} / \mathrm{s}$ ]

$7.9 \mathrm{MeV} \alpha$-particle scatters from a target material of atomic number 79 . From the given data the estimated diameter of nuclei of the target material is (approximately) $\_\_\_\_$ m.

$ \left[\frac{1}{4 \pi \epsilon_{\mathrm{o}}}=9 \times 10^9 \mathrm{Nm}^2 / \mathrm{C}^2 \text { and electron charge }=1.6 \times 10^{-19} \mathrm{C}\right] $

The energy of an electron in an orbit of the Bohr's atom is $-0.04E_0$ eV where $E_0$ is the ground state energy. If $L$ is the angular momentum of the electron in this orbit and $h$ is the Planck's constant, then

$ \frac{2\pi L}{h} $ is ________ :

If an alpha particle with energy 7.7 MeV is bombarded on a thin gold foil, the closest distance from nucleus it can reach is $\_\_\_\_$ m. (Atomic number of gold $=79$ and $\frac{1}{4 \pi \epsilon_{\mathrm{o}}}=9 \times 10^9$ in SI units)

Two radioactive substances A and B of mass numbers 200 and 212 respectively, shows spontaneous $\alpha$-decay with same $Q$ value of 1 MeV . The ratio of energies of $\alpha$-rays produced by A and B is $\_\_\_\_$ .

The energy released if hydrogen atoms are combined to form ${ }_2^4 \mathrm{He}$ is $\_\_\_\_$ MeV .

(Take binding energies per nucleon of ${ }_1^2 \mathrm{H}$ and ${ }_2^4 \mathrm{He}$ as 1.1 MeV and 7.2 MeV , respectively)

The ratio of momentum of the photons of the $1^{\text {st }}$ and $2^{\text {nd }}$ line of Balmer series of Hydrogen atoms is $\alpha / \beta$. The possible values of $\alpha$ and $\beta$ are:-

Assuming the experimental mass of ${ }_6^{12} C$ as $12 u$, the mass defect of ${ }_6^{12} C$ atom is $\_\_\_\_$ $\mathrm{MeV} / \mathrm{c}^2$.

(Mass of proton $=1.00727 \mathrm{u}$. mass of neutron $=1.00866 \mathrm{u}, 1 \mathrm{u}=931.5 \mathrm{MeV} / \mathrm{c}^2$ and c is the speed of the light in vacuum).

In the hydrogen atom, the electron makes a transition from the higher orbit (i) to a lower orbit $(f)$. The ratio of the radius of the orbits in given by $r_i: r_f=16: 4$. The wavelength of photon emitted due to this transition is $\_\_\_\_$ nm.

(Given Rydberg constant $=1.0973 \times 10^7 / \mathrm{m}$ )

In Rutherford's alpha-particle scattering experiment, only a few alpha particles rebound back because

A. The size of gold nucleus is very small as compared to the size of gold atom.

B. Alpha particle and gold nucleus have equal charge.

C. The impact parameter is minimum for a few alpha particles.

D. A few alpha particles have very high kinetic energy.

E. Only a few alpha particles undergo head-on collision with the nuclei.

Choose the correct answer from the options given below :

Two nuclei of mass number 3 combine with another nucleus of mass number 4 to yield a nucleus of mass number 10. If the binding energy per nucleon for the mass numbers 3,4 and 10 are $5.6 \mathrm{MeV}, 7.4 \mathrm{MeV}$ and 6.1 MeV , respectively, then in the process, $\Delta \mathrm{Mc}^2=$ $\_\_\_\_$ MeV .

The binding energy per nucleon of $^{209}_{83}Bi$ is _______ MeV.

[Take $m(^{209}_{83}Bi) = 208.980388\ \text{u}$, $m_p = 1.007825\ \text{u}$, $m_n = 1.008665\ \text{u}$, $1\ \text{u} = 931\ \text{MeV}/c^2$]

Angular momentum of an electron in a hydrogen atom is $\frac{3h}{\pi}$, then the energy of the electron is _____ eV.

For a nucleus of mass number A and radius R, the mass density of nucleus can be represented as

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A) : The density of the copper $(^ {64}_{29} \text{Cu})$ nucleus is greater than that of the carbon $(^ {12}_{6} \text{C})$ nucleus.

Reason (R) : The nucleus of mass number A has a radius proportional to $ A^{1/3} $.

In the light of the above statements, choose the most appropriate answer from the options given below :

In a hydrogen like ion, the energy difference between the $2^{\text {nd }}$ excitation energy state and ground is 108.8 eV . The atomic number of the ion is:

For a hydrogen atom, the ratio of the largest wavelength of Lyman series to that of the Balmer series is

A radioactive material $P$ first decays into $Q$ and then $Q$ decays to non-radioactive material $R$. Which of the following figure represents time dependent mass of $P, Q$ and $R$ ?

Given below are two statements :

Statement (I) : The dimensions of Planck's constant and angular momentum are same.

Statement (II) : In Bohr's model electron revolve around the nucleus only in those orbits for which angular momentum is integral multiple of Planck's constant.

In the light of the above statements, choose the most appropriate answer from the options given below :

Considering the Bohr model of hydrogen like atoms, the ratio of the radius of $5^{\text {th }}$ orbit of the electron in $\mathrm{Li}^{2+}$ and $\mathrm{He}^{+}$is

Given below are two statements: one is labelled as $\mathbf{A s s e r t i o n} \mathbf{A}$ and the other is labelled as Reason $\mathbf{R}$

Assertion A : The Bohr model is applicable to hydrogen and hydrogen-like atoms only.

Reason $\mathbf{R}$ : The formulation of Bohr model does not include repulsive force between electrons.

In the light of the above statements, choose the correct answer from the options given below

$ \text { Match the LIST-I with LIST-II } $

Considering Bohr's atomic model for hydrogen atom :

(A) the energy of H atom in ground state is same as energy of $\mathrm{He}^{+}$ion in its first excited state.

(B) the energy of H atom in ground state is same as that for $\mathrm{Li}^{++}$ ion in its second excited state.

(C) the energy of H atom in its ground state is same as that of $\mathrm{He}^{+}$ion for its ground state.

(D) the energy of $\mathrm{He}^{+}$ion in its first excited state is same as that for $\mathrm{Li}^{++}$ion in its ground state.

Choose the correct answer from the options given below :

The number of spectral lines emitted by atomic hydrogen that is in the 4th energy level, is

The frequency of revolution of the electron in Bohr's orbit varies with n, the principal quantum number as:

Choose the correct nuclear process from the below options [ p : proton, n : neutron, $\mathrm{e}^{-}$: electron, $\mathrm{e}^{+}$: positron, $v:$ neutrino, $\bar{v}:$ antineutrino]

The energy E and momentum p of a moving body of mass m are related by some equation. Given that c represents the speed of light, identify the correct equation

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A) : The binding energy per nucleon is found to be practically independent of the atomic number A , for nuclei with mass numbers between 30 and 170 .

Reason (R) : Nuclear force is long range. In the light of the above statements, choose the correct answer from the options given below :

A radioactive nucleus $\mathrm{n}_2$ has 3 times the decay constant as compared to the decay constant of another radioactive nucleus $n_1$. If initial number of both nuclei are the same, what is the ratio of number of nuclei of $n_2$ to the number of nuclei of $n_1$, after one half-life of $n_1$ ?

A nucleus at rest disintegrates into two smaller nuclei with their masses in the ratio of $2: 1$. After disintegration they will move :

The energy released in the fusion of $2 \mathrm{~kg}$ of hydrogen deep in the sun is $E_H$ and the energy released in the fission of $2 \mathrm{~kg}$ of ${ }^{235} \mathrm{U}$ is $E_U$. The ratio $\frac{E_H}{E_U}$ is approximately: (Consider the fusion reaction as $4_1^1H+2 \mathrm{e}^{-} \rightarrow{ }_2^4 \mathrm{He}+2 v+6 \gamma+26.7 \mathrm{~MeV}$, energy released in the fission reaction of ${ }^{235} \mathrm{U}$ is $200 \mathrm{~MeV}$ per fission nucleus and $\mathrm{N}_{\mathrm{A}}= 6.023 \times 10^{23})$

A hydrogen atom in ground state is given an energy of $10.2 \mathrm{~eV}$. How many spectral lines will be emitted due to transition of electrons?

The energy equivalent of $1 \mathrm{~g}$ of substance is :

If $M_0$ is the mass of isotope ${ }_5^{12} B, M_p$ and $M_n$ are the masses of proton and neutron, then nuclear binding energy of isotope is:

In a hypothetical fission reaction

${ }_{92} X^{236} \rightarrow{ }_{56} \mathrm{Y}^{141}+{ }_{36} Z^{92}+3 R$

The identity of emitted particles (R) is :

Binding energy of a certain nucleus is $18 \times 10^8 \mathrm{~J}$. How much is the difference between total mass of all the nucleons and nuclear mass of the given nucleus:

The longest wavelength associated with Paschen series is : (Given $\mathrm{R}_{\mathrm{H}}=1.097 \times 10^7 \mathrm{SI}$ unit)

The ratio of the shortest wavelength of Balmer series to the shortest wavelength of Lyman series for hydrogen atom is :

The angular momentum of an electron in a hydrogen atom is proportional to : (Where $\mathrm{r}$ is the radius of orbit of electron)

An electron rotates in a circle around a nucleus having positive charge $\mathrm{Ze}$. Correct relation between total energy (E) of electron to its potential energy (U) is :

According to Bohr's theory, the moment of momentum of an electron revolving in $4^{\text {th }}$ orbit of hydrogen atom is:

Which of the following nuclear fragments corresponding to nuclear fission between neutron $\left({ }_0^1 \mathrm{n}\right)$ and uranium isotope $\left({ }_{92}^{235} \mathrm{U}\right)$ is correct :

The mass number of nucleus having radius equal to half of the radius of nucleus with mass number 192 is :

If the wavelength of the first member of Lyman series of hydrogen is $\lambda$. The wavelength of the second member will be

An electron revolving in $n^{\text {th }}$ Bohr orbit has magnetic moment $\mu_n$. If $\mu_n \propto n^x$, the value of $x$ is

In a nuclear fission reaction of an isotope of mass $M$, three similar daughter nuclei of same mass are formed. The speed of a daughter nuclei in terms of mass defect $\Delta M$ will be :

The ratio of the magnitude of the kinetic energy to the potential energy of an electron in the 5^th excited state of a hydrogen atom is :

Given below are two statements:

Statement I : Most of the mass of the atom and all its positive charge are concentrated in a tiny nucleus and the electrons revolve around it, is Rutherford's model.

Statement II : An atom is a spherical cloud of positive charges with electrons embedded in it, is a special case of Rutherford's model.

In the light of the above statements, choose the most appropriate from the options given below

The explosive in a Hydrogen bomb is a mixture of ${ }_1 \mathrm{H}^2,{ }_1 \mathrm{H}^3$ and ${ }_3 \mathrm{Li}^6$ in some condensed form. The chain reaction is given by

$\begin{aligned} & { }_3 \mathrm{Li}^6+{ }_0 \mathrm{n}^1 \rightarrow{ }_2 \mathrm{He}^4+{ }_1 \mathrm{H}^3 \\ & { }_1 \mathrm{H}^2+{ }_1 \mathrm{H}^3 \rightarrow{ }_2 \mathrm{He}^4+{ }_0 \mathrm{n}^1 \end{aligned}$

During the explosion the energy released is approximately

[Given ; $\mathrm{M}(\mathrm{Li})=6.01690 \mathrm{~amu}, \mathrm{M}\left({ }_1 \mathrm{H}^2\right)=2.01471 \mathrm{~amu}, \mathrm{M}\left({ }_2 \mathrm{He}^4\right)=4.00388$ $\mathrm{amu}$, and $1 \mathrm{~amu}=931.5 \mathrm{~MeV}]$

The atomic mass of ${ }_6 \mathrm{C}^{12}$ is $12.000000 \mathrm{~u}$ and that of ${ }_6 \mathrm{C}^{13}$ is $13.003354 \mathrm{~u}$. The required energy to remove a neutron from ${ }_6 \mathrm{C}^{13}$, if mass of neutron is $1.008665 \mathrm{~u}$, will be :

The radius of third stationary orbit of electron for Bohr's atom is R. The radius of fourth stationary orbit will be:

Given below are two statements: one is labelled as Assertion $\mathbf{A}$ and the other is labelled as Reason $\mathbf{R}$

Assertion A : The binding energy per nucleon is practically independent of the atomic number for nuclei of mass number in the range 30 to 170 .

Reason R : Nuclear force is short ranged.

In the light of the above statements, choose the correct answer from the options given below

$_{92}^{238}A \to _{90}^{234}B + _2^4D + Q$

In the given nuclear reaction, the approximate amount of energy released will be:

[Given, mass of ${ }_{92}^{238} \mathrm{~A}=238.05079 \times 931.5 ~\mathrm{MeV} / \mathrm{c}^{2},$

mass of ${ }_{90}^{234} B=234 \cdot 04363 \times 931 \cdot 5 ~\mathrm{MeV} / \mathrm{c}^{2},$

mass of $\left.{ }_{2}^{4} D=4 \cdot 00260 \times 931 \cdot 5 ~\mathrm{MeV} / \mathrm{c}^{2}\right]$

A $12.5 \mathrm{~eV}$ electron beam is used to bombard gaseous hydrogen at room temperature. The number of spectral lines emitted will be:

The energy of $\mathrm{He}^{+}$ ion in its first excited state is, (The ground state energy for the Hydrogen atom is $-13.6 ~\mathrm{eV})$ :

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 $\lambda_{A}$ and $\lambda_{B}$ are decay constants of A and B respectively, then choose the correct relation from the given options.

The half life of a radioactive substance is T. The time taken, for disintegrating $\frac{7}{8}$th part of its original mass will be:

The angular momentum for the electron in Bohr's orbit is L. If the electron is assumed to revolve in second orbit of hydrogen atom, then the change in angular momentum will be

A radio active material is reduced to $1 / 8$ of its original amount in 3 days. If $8 \times 10^{-3} \mathrm{~kg}$ of the material is left after 5 days the initial amount of the material is

The waves emitted when a metal target is bombarded with high energy electrons are

For a nucleus ${ }_{\mathrm{A}}^{\mathrm{A}} \mathrm{X}$ having mass number $\mathrm{A}$ and atomic number $\mathrm{Z}$

A. The surface energy per nucleon $\left(b_{\mathrm{s}}\right)=-a_{1} A^{2 / 3}$.

B. The Coulomb contribution to the binding energy $\mathrm{b}_{\mathrm{c}}=-a_{2} \frac{Z(Z-1)}{A^{4 / 3}}$

C. The volume energy $\mathrm{b}_{\mathrm{v}}=a_{3} A$

D. Decrease in the binding energy is proportional to surface area.

E. While estimating the surface energy, it is assumed that each nucleon interacts with 12 nucleons. ( $a_{1}, a_{2}$ and $a_{3}$ are constants)

Choose the most appropriate answer from the options given below:

A small particle of mass $m$ moves in such a way that its potential energy $U=\frac{1}{2} m ~\omega^{2} r^{2}$ where $\omega$ is constant and $r$ is the distance of the particle from origin. Assuming Bohr's quantization of momentum and circular orbit, the radius of $n^{\text {th }}$ orbit will be proportional to,

The energy levels of an hydrogen atom are shown below. The transition corresponding to emission of shortest wavelength is :

An electron of a hydrogen like atom, having $Z=4$, jumps from $4^{\text {th }}$ energy state to $2^{\text {nd }}$ energy state. The energy released in this process, will be :

(Given Rch = $13.6~\mathrm{eV}$)

Where R = Rydberg constant

c = Speed of light in vacuum

h = Planck's constant

The mass of proton, neutron and helium nucleus are respectively $1.0073~u,1.0087~u$ and $4.0015~u$. The binding energy of helium nucleus is :

A free neutron decays into a proton but a free proton does not decay into neutron. This is because

Speed of an electron in Bohr's $7^{\text {th }}$ orbit for Hydrogen atom is $3.6 \times 10^{6} \mathrm{~m} / \mathrm{s}$. The corresponding speed of the electron in $3^{\text {rd }}$ orbit, in $\mathrm{m} / \mathrm{s}$ is :

Substance A has atomic mass number 16 and half life of 1 day. Another substance B has atomic mass number 32 and half life of $\frac{1}{2}$ day. If both A and B simultaneously start undergo radio activity at the same time with initial mass 320 g each, how many total atoms of A and B combined would be left after 2 days.

If a radioactive element having half-life of $30 \mathrm{~min}$ is undergoing beta decay, the fraction of radioactive element remains undecayed after $90 \mathrm{~min}$. will be

The energy levels of an atom is shown in figure.

Which one of these transitions will result in the emission of a photon of wavelength 124.1 nm?

Given (h = 6.62 $\times$ 10$^{-34}$ Js)

The ratio of the density of oxygen nucleus ($_8^{16}O$) and helium nucleus ($_2^{4}\mathrm{He}$) is

A photon is emitted in transition from n = 4 to n = 1 level in hydrogen atom. The corresponding wavelength for this transition is (given, h = 4 $\times$ 10$^{-15}$ eVs) :

Consider the following radioactive decay process

$_{84}^{218}A\buildrel \alpha \over \longrightarrow {A_1}\buildrel {{\beta ^ - }} \over \longrightarrow {A_2}\buildrel \gamma \over \longrightarrow {A_3}\buildrel \alpha \over \longrightarrow {A_4}\buildrel {{\beta ^ + }} \over \longrightarrow {A_5}\buildrel \gamma \over \longrightarrow {A_6}$

The mass number and the atomic number of A$_6$ are given by :

Read the following statements :

(A) Volume of the nucleus is directly proportional to the mass number.

(B) Volume of the nucleus is independent of mass number.

(C) Density of the nucleus is directly proportional to the mass number.

(D) Density of the nucleus is directly proportional to the cube root of the mass number.

(E) Density of the nucleus is independent of the mass number.

Choose the correct option from the following options.

Find the ratio of energies of photons produced due to transition of an electron of hydrogen atom from its (i) second permitted energy level to the first level, and (ii) the highest permitted energy level to the first permitted level.

A radioactive sample decays $\frac{7}{8}$ times its original quantity in 15 minutes. The half-life of the sample is

The half life period of a radioactive substance is 60 days. The time taken for $\frac{7}{8}$th of its original mass to disintegrate will be :

The activity of a radioactive material is $6.4 \times 10^{-4}$ curie. Its half life is 5 days. The activity will become $5 \times 10^{-6}$ curie after :

What is the half-life period of a radioactive material if its activity drops to $1 / 16^{\text {th }}$ of its initial value in 30 years?

A nucleus of mass $M$ at rest splits into two parts having masses $\frac{M^{\prime}}{3}$ and ${{2M'} \over 3}(M' < M)$. The ratio of de Broglie wavelength of two parts will be :

Mass numbers of two nuclei are in the ratio of $4: 3$. Their nuclear densities will be in the ratio of

The disintegration rate of a certain radioactive sample at any instant is 4250 disintegrations per minute. 10 minutes later, the rate becomes 2250 disintegrations per minute. The approximate decay constant is :

$\left(\right.$Take $\left.\log _{10} 1.88=0.274\right)$

Hydrogen atom from excited state comes to the ground state by emitting a photon of wavelength $\lambda$. The value of principal quantum number '$n$' of the excited state will be : ($\mathrm{R}:$ Rydberg constant)

The momentum of an electron revolving in $\mathrm{n}^{\text {th }}$ orbit is given by :

(Symbols have their usual meanings)

The magnetic moment of an electron (e) revolving in an orbit around nucleus with an orbital angular momentum is given by :

A hydrogen atom in ground state absorbs 12.09 eV of energy. The orbital angular momentum of the electron is increased by :

In the following nuclear reaction,

$D\buildrel \alpha \over \longrightarrow {D_1}\buildrel {{\beta ^ - }} \over \longrightarrow {D_2}\buildrel \alpha \over \longrightarrow {D_3}\buildrel \gamma \over \longrightarrow {D_4}$

Mass number of D is 182 and atomic number is 74. Mass number and atomic number of D₄ respectively will be _________.

The activity of a radioactive material is 2.56 $\times$ 10^$-$3 Ci. If the half life of the material is 5 days, after how many days the activity will become 2 $\times$ 10^$-$5 Ci ?

Following statements related to radioactivity are given below :

(A) Radioactivity is a random and spontaneous process and is dependent on physical and chemical conditions.

(B) The number of un-decayed nuclei in the radioactive sample decays exponentially with time.

(C) Slope of the graph of log_e (no. of undecayed nuclei) Vs. time represents the reciprocal of mean life time ($\tau$).

(D) Product of decay constant ($\lambda$) and half-life time (T_1/2) is not constant.

Choose the most appropriate answer from the options given below :

The Q-value of a nuclear reaction and kinetic energy of the projectile particle, K_p are related as :

Given below are two statements :

Statement I : In hydrogen atom, the frequency of radiation emitted when an electron jumps from lower energy orbit (E₁) to higher energy orbit (E₂), is given as hf = E₁ $-$ E₂

Statement II : The jumping of electron from higher energy orbit (E₂) to lower energy orbit (E₁) is associated with frequency of radiation given as f = (E₂ $-$ E₁)/h

This condition is Bohr's frequency condition.

In the light of the above statements, choose the correct answer from the options given below :

A hydrogen atom in its ground state absorbs 10.2 eV of energy. The angular momentum of electron of the hydrogen atom will increase by the value of :

(Given, Planck's constant = 6.6 $\times$ 10^$-$34 Js).

A radioactive nucleus can decay by two different processes. Half-life for the first process is 3.0 hours while it is 4.5 hours for the second process. The effective half-life of the nucleus will be:

How many alpha and beta particles are emitted when Uranium ₉₂U²³⁸ decays to lead ₈₂Pb²⁰⁶ ?

Which of the following figure represents the variation of ${l_n}\left( {{R \over {{R_0}}}} \right)$ with ${l_n}A$ (if R = radius of a nucleus and A = its mass number)

The ratio for the speed of the electron in the 3^rd orbit of He⁺ to the speed of the electron in the 3^rd orbit of hydrogen atom will be :

In Bohr's atomic model of hydrogen, let K, P and E are the kinetic energy, potential energy and total energy of the electron respectively. Choose the correct option when the electron undergoes transitions to a higher level :

Choose the correct option from the following options given below :

Nucleus A is having mass number 220 and its binding energy per nucleon is 5.6 MeV. It splits in two fragments 'B' and 'C' of mass numbers 105 and 115. The binding energy of nucleons in 'B' and 'C' is 6.4 MeV per nucleon. The energy Q released per fission will be :

The binding energy per nucleon for the parent nucleus is ${E_1}$ and that for the daughter nuclei is ${E_2}.$ Then

The speed of daughter nuclei is

The above is a plot of binding energy per nucleon ${E_b},$ against the nuclear mass $M;A,B,C,D,E,F$ correspond to different nuclei. Consider four reactions :
$\eqalign{ & \left( i \right)\,\,\,\,\,\,\,\,\,\,A + B \to C + \varepsilon \,\,\,\,\,\,\,\,\,\,\left( {ii} \right)\,\,\,\,\,\,\,\,\,\,C \to A + B + \varepsilon \,\,\,\,\,\,\,\,\,\, \cr & \left( {iii} \right)\,\,\,\,\,\,D + E \to F + \varepsilon \,\,\,\,\,\,\,\,\,\,\left( {iv} \right)\,\,\,\,\,\,\,\,\,F \to D + E + \varepsilon ,\,\,\,\,\,\,\,\,\,\, \cr} $

where $\varepsilon $ is the energy released? In which reactions is $\varepsilon $ positive?

Statement- 2:
For heavy nuclei, binding energy per nucleon increases with increasing $Z$ while for light nuclei it decreases with increasing $Z.$

Then which of the following is true?

Then $Z$ of the resulting nucleus is