Atoms and Nuclei

In an alpha particle scattering experiment distance of closest approach for the \(\alpha\) particle is \(4.5 \times 10^{-14} \mathrm{~m}\). If target nucleus has atomic number 80 , then maximum velocity of \(\alpha\)-particle 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 :

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:

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

Radius of a certain orbit of hydrogen atom is 8.48 \(\mathop A\limits^o\). If energy of electron in this orbit is \(E / x\). then \(x=\) ________ (Given \(\mathrm{a}_0=0.529\) \(\mathop A\limits^o\), \(E=\) energy of electron in ground stat...

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

If three helium nuclei combine to form a carbon nucleus then the energy released in this reaction is
________ \(\times 10^{-2} \mathrm{~MeV}\). (Given \(1 \mathrm{u}=931 \mathrm{~MeV} / \mathrm{c}^2\), atomic mass of helium $$=4.002603 \mat...

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 :

The shortest wavelength of the spectral lines in the Lyman series of hydrogen spectrum is \(915\mathop A\limits^o\). The longest wavelength of spectral lines in the Balmer series will be _______ \(\mathop A\limits^o\).

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

A hydrogen atom changes its state from \(n=3\) to \(n=2\). Due to recoil, the percentage change in the wave length of emitted light is approximately \(1 \times 10^{-n}\). The value of \(n\) is _______. [Given Rhc $$=13.6 \mathrm{~eV}, \math...

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 :

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

The disintegration energy \(Q\) for the nuclear fission of \({ }^{235} \mathrm{U} \rightarrow{ }^{140} \mathrm{Ce}+{ }^{94} \mathrm{Zr}+n\) is
_______ \(\mathrm{MeV}\).
Given atomic masses of $${ }^{235} \mathrm{U}: 235.0439 u ;{ }^{140} \m...

The mass defect in a particular reaction is \(0.4 \mathrm{~g}\). The amount of energy liberated is \(n \times 10^7 \mathrm{~kWh}\), where \(n=\) __________. (speed of light \(\left.=3 \times 10^8 \mathrm{~m} / \mathrm{s}\right)\)

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

A nucleus has mass number \(A_1\) and volume \(V_1\). Another nucleus has mass number \(A_2\) and Volume \(V_2\). If relation between mass number is \(A_2=4 A_1\), then \(\frac{V_2}{V_1}=\) __________.

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

A electron of hydrogen atom on an excited state is having energy \(\mathrm{E}_{\mathrm{n}}=-0.85 \mathrm{~eV}\). The maximum number of allowed transitions to lower energy level is _________.

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

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

When a hydrogen atom going from \(n=2\) to \(n=1\) emits a photon, its recoil speed is \(\frac{x}{5} \mathrm{~m} / \mathrm{s}\). Where \(x=\) ________. (Use, mass of hydrogen atom \(=1.6 \times 10^{-27} \mathrm{~kg}\))

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 \righta...

Hydrogen atom is bombarded with electrons accelerated through a potential difference of \(\mathrm{V}\), which causes excitation of hydrogen atoms. If the experiment is being performed at \(\mathrm{T}=0 \mathrm{~K}\), the minimum potential d...

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 clou...

In a nuclear fission process, a high mass nuclide \((A \approx 236)\) with binding energy \(7.6 \mathrm{~MeV} /\) Nucleon dissociated into middle mass nuclides \((\mathrm{A} \approx 118)\), having binding energy of $$8.6 \mathrm{~MeV} / \ma...

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

If Rydberg's constant is \(R\), the longest wavelength of radiation in Paschen series will be \(\frac{\alpha}{7 R}\), where \(\alpha=\) ________.

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....

The radius of a nucleus of mass number 64 is 4.8 fermi. Then the mass number of another nucleus having radius of 4 fermi is $\frac{1000}{x}$, where $x$ is _______.

The minimum energy required by a hydrogen atom in ground state to emit radiation in Balmer series is nearly :

A particular hydrogen-like ion emits the radiation of frequency $3 \times 10^{15} \mathrm{~Hz}$ when it makes transition from $n=2$ to $n=1$. The frequency of radiation emitted in transition from $n=3$ to $n=1$ is $\frac{x}{9} \times 10^{15...

From the statements given below :
(A) The angular momentum of an electron in $n^{\text {th }}$ orbit is an integral multiple of $\hbar$.
(B) Nuclear forces do not obey inverse square law.
(C) Nuclear forces are spin dependent.
(D) Nuclear f...

A nucleus with mass number 242 and binding energy per nucleon as \(7.6~ \mathrm{MeV}\) breaks into two fragment each with mass number 121. If each fragment nucleus has binding energy per nucleon as \(8.1 ~\mathrm{MeV}\), the total gain in b...

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 ratio of wavelength of spectral lines \(\mathrm{H}_{\alpha}\) and \(\mathrm{H}_{\beta}\) in the Balmer series is \(\frac{x}{20}\). The value of \(x\) is _________.

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

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 radius of fifth orbit of the \(\mathrm{Li}^{++}\) is __________ \(\times 10^{-12} \mathrm{~m}\).
Take: radius of hydrogen atom \(= 0.51\,\mathop A\limits^o\)

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

Experimentally it is found that \(12.8 ~\mathrm{eV}\) energy is required to separate a hydrogen atom into a proton and an electron. So the orbital radius of the electron in a hydrogen atom is \(\frac{9}{x} \times 10^{-10} \mathrm{~m}\). The...

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 ...

For hydrogen atom, \(\lambda_{1}\) and \(\lambda_{2}\) are the wavelengths corresponding to the transitions 1 and 2 respectively as shown in figure. The ratio of \(\lambda_{1}\) and \(\lambda_{2}\) is \(\frac{x}{32}\). The value of \(x\) is...

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

If the binding energy of ground state electron in a hydrogen atom is $13.6\, \mathrm{eV}$, then, the energy required to remove the electron from the second excited state of $\mathrm{Li}^{2+}$ will be : $x \times 10^{-1} \mathrm{eV}$. The va...

The radius of electron's second stationary orbit in Bohr's atom is R. The radius of 3rd orbit will be

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 :

A radioactive nucleus decays by two different process. The half life of the first process is 5 minutes and that of the second process is $30 \mathrm{~s}$. The effective half-life of the nucleus is calculated to be $\frac{\alpha}{11} \mathrm...

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

Assertion A: The nuclear density of nuclides ${ }_{5}^{10} \mathrm{~B},{ }_{3}^{6} \mathrm{Li},{ }_{26}^{56} \mathrm...