Atoms and Nuclei

In Geiger-Marsden experiment, the number of scattered $\alpha$-particles $N(\theta)$ is plotted as a function of scattering angle $\theta$. Which of the following options represents the correct plot?

Consider the following nuclear reaction
\({ }^{238} \mathrm{U} \longrightarrow{ }^{234} \mathrm{Th}+{ }^4 \mathrm{He}\)
Take masses of ${ }^{238} \mathrm{U},{ }^{234} \mathrm{Th}$ and ${ }^4 \mathrm{He}$ as $238.050 \mathrm{u}, 234.043 \m...

Consider that an electron is revolving in an excited state of Hydrogen atom with velocity $\sqrt{25.6} \times 10^5 \mathrm{~ms}^{-1}$. The radius of the orbit is $x \times 10^{-9} \mathrm{~m}$. The value of $x$ is:
[Take the mass of electro...

An unknown nucleus has a nuclear density of $2.29 \times 10^{17} \mathrm{~kg} / \mathrm{m}^3$ and mass of $19.926 \times 10^{-27} \mathrm{~kg}$. Its mass number $A$ is approximately:
(Take $R_0=1.2 \times 10^{-15} \mathrm{~m}, 4 \pi=12.56$ ...

Four statements are given ( $A$ is mass number):
A. The volume of a nucleus is proportional to $A^{1 / 3}$.
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...

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 \mathrm{eV}=1.6 \times 10^{-19} \mathrm{~J}, \mathrm{...

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 of the $n^{\text {th }}$ orbit and the particle's speed $v$ in the orbit de...

Some energy levels of a molecule are shown in the figure with their wavelengths of transitions. Then :

Select the correct statements among the following :
A. Slow neutrons can cause fission in \({ }_{92}^{235} \mathrm{U}\) than fast neutrons.
B. \(\alpha\)-rays are Helium nuclei.
C. \(\beta\)-rays are fast moving electrons or positrons.
D. $...

Water is used as a coolant in a nuclear reactor because of its

The spectral series which corresponds to the electronic transition from the levels \(n_2=5,6, \ldots\) to the level \(n_1=4\) is

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 o...

\({ }_{82}^{290} X \xrightarrow{\alpha} Y \xrightarrow{e^{+}} Z \xrightarrow{\beta^{-}} P \xrightarrow{e^{-}} Q\)
In the nuclear emission stated above, the mass number and atomic number of the product \(Q\) respectively, are

Match List I with List II:

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The angular momentum of an electron moving in an orbit of hydrogen atom is \(\mathrm{1.5\left(\frac{h}{\pi}\right)}\). The energy in the same orbit is nearly.

The wavelength of Lyman series of hydrogen atom appears in:

The ground state energy of hydrogen atom is \(-13.6 ~\mathrm{eV}\). The energy needed to ionize hydrogen atom from its second excited state will be :

The radius of inner most orbit of hydrogen atom is \(5.3 \times 10^{-11} \mathrm{~m}\). What is the radius of third allowed orbit of hydrogen atom?

In hydrogen spectrum, the shortest wavelength in the Balmer series is \(\lambda\). The shortest wavelength in the Bracket series is :

The half life of a radioactive substance is 20 minutes. In how much time, the activity of substance drops to \(\left(\frac{1}{16}\right)^{\text {th }}\) of its initial value?

The ratio of Coulomb's electrostatic force to the gravitational force between an electron and a proton separated by some distance is 2.4 \(\times\) 1039. The ratio of the proportionality constant, \(K = {1 \over {4\pi {\varepsilon _0}}}\) t...

At any instant, two elements X1 and X2 have same number of radioactive atoms. If the decay constant of X1 and X2 are 10 \(\lambda\) and \(\lambda\) respectively, then the time when the ratio of their atoms becomes \({1 \over e}\) respective...

Given below are two statements
Statement I : The law of radioactive decay states that the number of nuclei undergoing the decay per unit time is inversely proportional to the total number of nuclei in the sample.
Statement II : The half of ...

Let R1 be the radius of the second stationary orbit and R2 be the radius of the fourth stationary orbit of an electron in Bohr's model. The ratio \({{{R_1}} \over {{R_2}}}\) is :

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

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

In the given nuclear reaction, the element X is
\({}_{11}^{22}Na \to X + {e^ + } + v\)

The graph which shows the variation of the de Broglie wavelength (\(\lambda\)) of a particle and its associated momentum (p) is

A radioactive nucleus \(_Z^AX\) \(\to\) \({}_{Z - 1}B\) \(\to\) \({}_{Z - 3}C\) \(\to\) \({}_{Z - 2}D\), 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 activity 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 per nucleon of unfragmented nuclei is 7.6MeV while that of fragments is 8.5MeV. The total gain in the Binding Energy in the process is :

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

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

The energy equivalent of 0.5 g of a substance is :

\(\alpha\)-particale consists of :

The total energy of an electron in an atom in an orbit is –3.4 eV. Its kinetic and potential energies are, respectively.

For a radioactive material, half-life is 10
minutes. If initially there are 600 number of
nuclei, the time taken (in minutes) for the
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 same number of nuclei. After what time, the ratio of number of nuclei of material 'B' to that 'A' will be 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

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

When an \(\alpha\)-particle of mass m moving with velocity v bombards on a heavy nucleus of charge Ze, its distance of closest approach from the nucleus depends on m as

Given the value of Rydberg constant is 107 m\(-\)1, the wave number of the last line of the Balmer series in hydrogen spectrum will be

If radius of the \({}_{13}^{27}\) Al nucleus is taken to be RAl, then the radius of \({}_{53}^{125}\)Te nucleus is nearly

Consider 3rd orbit of He+ (Helium), using non-relativistic approach, the speed of electron in this orbit will be [given K = 9 \(\times\) 109 constant, Z = 2 and h (Planck's Constant) = 6.6 \(\times\) 10\(-\)34 J s]

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

The binding energy per nucleon of and nuclei are 5.60 MeV and 7.06 MeV respectively. In the nuclear reaction
\({}_3^7Li + {}_1^1H \to {}_2^4He + _2^4He + Q\)
the value of energy Q released is

Hydrogen atom in ground state is excited by a monochromatic radiation of \(\lambda\) = 975 \(\mathop A\limits^ \circ\). Number of spectral lines in the resulting spectrum emitted will be