Atoms and Nuclei

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 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:-

The energy released when $\frac{7}{17.13} \mathrm{~kg}$ of ${ }_3^7 \mathrm{Li}$ is converted into ${ }_2^4 \mathrm{He}$ by proton bombardment is $\alpha \times 10^{32} \mathrm{eV}$. The value of $\alpha$ is $\_\_\_\_$ . (Nearest integer) (...

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)

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 $\_\_\_\_...

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 ...

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 , respect...

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. T...

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

Using Bohr’s model, calculate the ratio of the magnetic fields generated due to the motion of the electrons in the 2nd and 4th orbits of hydrogen atom ________.

The binding energy per nucleon of $^{209}_{83}Bi$ is _______ MeV.[Take $m(^{209}_{83}Bi) = 208.980388\ \text{u}$, $m_p = 1.007825\ \text{u}$, $m_n = 1.008665\ \text{u}$, $1\ \text{u} = 931\ \text{MeV}/c^2$]

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 :

A nucleus has mass number $\alpha$ and radius $R_{\alpha}$. Another nucleus has mass number $\beta$ and radius $R_{\beta}$.If $\beta = 8\alpha$ then $R_{\alpha} / R_{\beta}$ 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 o...

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 w...

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...

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 ...

The average energy released per fission for the nucleus of ${ }_{92}^{235} \mathrm{U}$ is 190 MeV . When all the atoms of 47 g pure ${ }_{92}^{235} \mathrm{U}$ undergo fission process, the energy released is $\alpha \times 10^{23} \mathrm{M...

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

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 \time...

$7.9 \mathrm{MeV} \alpha$-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{...

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

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)

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 __...

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

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

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:

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 $(^ {12}_{6} \text{C})$...

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 :
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 inte...

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 $R$ ?

\(\text { Match the LIST-I with LIST-II }\)


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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...

An electron in the hydrogen atom initially in the fourth excited state makes a transition to $\mathrm{n}^{\text {th }}$ energy state by emitting a photon of energy 2.86 eV . The integer value of n will be__________.

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}^{++...

Assuming the validity of Bohr's atomic model for hydrogen like ions the radius of $\mathrm{Li}^{++}$ ion in its ground state is given by $\frac{1}{X} a_0$, where $X=$ __________ (Where $\mathrm{a}_0$ is the first Bohr's radius.)

Energy released when two deuterons $\left({ }_1 \mathrm{H}^2\right)$ fuse to form a helium nucleus $\left({ }_2 \mathrm{He}^4\right)$ is :
(Given : Binding energy per nucleon of ${ }_1 \mathrm{H}^2=1.1 \mathrm{MeV}$ and binding energy per n...

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

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

During the transition of electron from state A to state C of a Bohr atom, the wavelength of emitted radiation is $2000 \mathop A\limits^o$ and it becomes $6000 \mathop A\limits^o$ when the electron jumps from state B to state C. Then the wa...

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

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...

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 nu...

A star has \(100 \%\) helium composition. It starts to convert three \({ }^4 \mathrm{He}\) into one \({ }^{12} \mathrm{C}\) via triple alpha process as $${ }^4 \mathrm{He}+{ }^4 \mathrm{He}+{ }^4 \mathrm{He} \rightarrow{ }^{12} \mathrm{C}+\...

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

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 approximate...

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

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?

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: