Atoms and Nuclei

The half-life of Au198 is 2.7 days. The activity of 1.50 mg of Au198 if its atomic weight is 198 g mol\(-\)1 is, (Na = 6 \(\times\) 1023/mol).

The energy required to ionise a hydrogen like
ion in its ground state is 9 Rydbergs. What is
the wavelength of the radiation emitted when
the electron in this ion jumps from the second
excited state to the ground state ?

The graph which depicts the results of
Rutherford gold foil experiment with
\(\alpha\)-particales is :
\(\theta\) : Scattering angle
Y : Number of scattered \(\alpha\)-particles detected
(Plots are schematic and not to scale)

The first member of the Balmer series of
hydrogen atom has a wavelength of 6561 Å.
The wavelength of the second member of the
Balmer series (in nm) is:

The time period of revolution of electron in its ground state orbit in a hydrogen atom is 1.6 \(\times\) 10-16 s. The frequency of revolution of the electron in its first excited state (in s-1) is :

The activity of a radioactive sample falls from 700 s–1 to 500 s–1 in 30 minutes. Its half life is close
to:

You are given that Mass of \({}_3^7Li\) = 7.0160u,
Mass of \({}_2^4He\) = 4.0026u
and Mass of \({}_1^1H\) = 1.0079u.
When 20 g of \({}_3^7Li\) is converted into \({}_2^4He\) by proton capture, the energy liberated, (in kWh), is :
[Mass of n...

Given the masses of various atomic particles
mp = 1.0072 u, mn = 1.0087 u, me = 0.000548 u,
\({m_{\overline v }}\) = 0, md = 2.0141 u, where p \(\equiv\) proton,
n \(\equiv\) neutron, e \(\equiv\) electron, \(\overline v\) $$ \equiv ...

Activities of three radioactive substances A, B
and C are represented by the curves A, B and
C, in the figure. Then their half-lives
\({T_{{1 \over 2}}}\left( A \right)\) : \({T_{{1 \over 2}}}\left( B \right)\) : $${T_{{1 \over 2}}}\left( C...

A particle of mass 200 MeV/c2 collides with a
hydrogen atom at rest. Soon after the collision
the particle comes to rest, and the atom
recoils and goes to its first excited state. The
initial kinetic energy of the particle (in eV) is
$${N \...

A radioactive nucleus decays by two different
processes. The half life for the first process is
10 s and that for the second is 100 s. The
effective half life of the nucleus is close to :

Find the Binding energy per neucleon for \({}_{50}^{120}Sn\). Mass of proton mp
= 1.00783 U, mass of neutron
mn
= 1.00867 U and mass of tin nucleus mSn = 119.902199 U. (take 1U = 931 MeV)

In a radioactive material, fraction of active
material remaining after time t is 9/16. The
fraction that was remaining after t/2 is

Hydrogen ion and singly ionized helium atom are accelerated, from rest, through the same potential
difference. The ratio of final speeds of hydrogen and helium ions is close to :

The radius R of a nucleus of mass number A can be estimated by the formula R = (1.3 \(\times\) 10–15)A1/3 m.
It follows that the mass density of a nucleus is of the order of :
(Mprot. \(\cong\) Mneut \(\simeq\) 1.67 \(\times\) 10–27...

In a reactor, 2 kg of 92U235 fuel is fully used up
in 30 days. The energy released per fission is
200 MeV. Given that the Avogadro number,
N = 6.023 \(\times\) 1026 per kilo mole and 1 eV =
1.6 × 10–19 J. The power output of the reactor i...

In a hydrogen atom the electron makes a
transition from (n + 1)th level to the nth level.
If n >> 1, the frequency of radiation emitted is
proportional to :

A sample of radioactive material A, that has an activity of 10 mCi(1 Ci = 3.7 \(\times\) 1010 decays/s), has twice the number of nuclei as another sample of a different radioactive materail B which has an activity of 20 mCi. The correct c...

At a given instant, say t = 0, two radioactive substance A and B have equal activities. the ratio \({{{R_B}} \over {{R_A}}}\) of their activities after time t itself decays with time t as e\(-\)3t. If the half-life of A is ln2, the half-li...

Taking the wavelength of first Balmer line in
hydrogen spectrum (n = 3 to n = 2) as 660 nm,
the wavelength of the 2nd Balmer line (n = 4 to
n = 2) will be :

A He+ ion is in its first excited state. Its
ionization energy is :-

Radiation coming from transitions
n = 2 to n = 1 of hydrogen atoms fall on He+
ions in n = 1 and n = 2 states. The possible
transition of helium ions as they absorb energy
from the radiation is :

The ratio of mass densities of nuclei of 40Ca
and 16O is close to :-

A particle of mass m moves in a circular orbit in a central potential field U(r) = \({1 \over 2}\) kr2. If Bohr 's
quantization conditions are applied, radii of possible orbitls and energy levels vary with quantum number n as :

In a radioactive decay chain, the initial nucleus is \({}_{90}^{232}\)Th. At the end there are 6 \(\alpha\)-particles and 4 \(\beta\)-particles which are emitted. If the end nucleus is \({}_Z^A\)X, A and Z are given by :

An excited He+
ion emits two photons in succession, with wavelengths 108.5 nm and 30.4 nm, in making a
transition to ground state. The quantum number n, corresponding to its initial excited state is (for photon of
wavelength \(\lambda\), ...

Half lives of two radioactive nuclei A and B are 10 minutes and 20 minutes, respectively, If initially a sample
has equal number of nuclei, then after 60 minutes, the ratio of decayed numbers of nuclei A and B will be :

Consider an electron in a hydrogen atom revolving in its second excited state (having radius 4.65 \(\mathop A\limits^o\)). The
de-Broglie wavelength of this electron is :

The electron in a hydrogen atom first jumps from the third excited state to the second excited state and
subsequently to the first excited state. The ratio of the respective wavelengths, \({{{\lambda _1}} \over {{\lambda _2}}}\), of the pho...

A hydrogen atom, initially in the ground state is excited by absorbing a photon of wavelength 980\(\mathop A\limits^ \circ\). The radius of the atom in the excited state, in terms of Bohr radius a0 will be : (hc = 12500 eV$$\mathop A\limi...

In a hydrogen like atom, when an electron jumps from the M-shell to the L-shell, the wavelength of emitted radiation is \(\lambda\). If an electron jumps from N-shell to the L-shell, the wavelength of emitted radiation will be:

Using a nuclear counter the count rate of emitted particles from a radioactive source is measured. At t = 0 it was 1600 counts per second and t = 8 seconds it was 100 counts per second. The count rate observed, as counts per second, at t = ...

Consider the nuclear fission
Ne20 \(\to\) 2He4 + C12
Given that the binding energy/ nucleon of Ne20, He4 and C12 are, respectively, 8.03 MeV, 7.07 MeV and 7.86 MeV, identify the correct statement -

Two radioactive materials A and B have decay
constants 10\(\lambda\) and \(\lambda\), respectively. It initially
they have the same number of nuclei, then the
ratio of the number of nuclei of A to that of B
will be 1/e after a time :

In Li+ +, electron in first Bohr orbit is excited to a level by a radiation of wavelength \(\lambda\). When the ion gets
deexcited to the ground state in all possible ways (including intermediate emissions), a total of six spectral
lines a...

Two radioactive substances A and B have decay constants 5\(\lambda\) and \(\lambda\) respectively. At t = 0, a sample has the
same number of the two nuclei. The time taken for the ratio of the number of nuclei to become $${\left( {{1 \ove...

At some instant, a radioactive sample S1 having an activity 5 \(\mu\)Ci has twice the number of nuclei as another sample S2 which has an activity of 10 \(\mu\)Ci. The half lives of S1 and S2 are :

A solution containing active cobalt \({^{60}_{27}}Co\) having activity of \(0.8\) \(\mu Ci\) and decay constant \(\lambda\) is injected in an animal's body. If \(1\,c{m^3}\) of blood is drawn from the animal's body after \(10\) hrs of inje...

The energy required to remove the electron from a singly ionized Helium atom is \(2.2\) times the energies required to remove an electron from Helium atom. The total energy required to ionize the Helium atom completely is :

Muon (\(\mu\)\(-\)) is a negatively charged (|q| = |e|) particle with a mass m\(\mu\) = 200 me, where me is the mass of the electron and e is the electronic charge. If \(\mu\)\(-\) is bond to a proton to form a hydrogen like atom, ident...

An unstable heavy nucleus at rest breaks into two nuclei which move away with velocities in the ratio of 8 : 27. The ratio of the radii of the nuclei (assumed to be spherical) is :

An electron from various excited states of hydrogen atom emit radiation to come to the ground state. Let
\({\lambda _n}\), \({\lambda _g}\) be the de Broglie wavelength of the electron in the nth state and the ground state respectively. Let...

If the series limit frequency of the Lyman series is \({\nu _L}\), then the series limit frequency of the Pfund series is:

It is found that if a neutron suffers an elastic collinear collision with deuterium at rest, fractional loss of its
energy is pd; while for its similar collision with carbon nucleus at rest, fractional loss of energy is pc. The values of pd...

Imagine that a reactor converts all given mass into energy and that it operates at a power level of 109 watt. The mass of the fuel consumed per hour in the reactor will be : (velocity of light, c is
3×108 m/s)

The acceleration of an electron in the first orbit of the hydrogen atom (n = 1) is :

According to Bohr’s theory, the time averaged magnetic field at the centre (i.e. nucleus) of a hydrogen atom due to the motion of electrons in the nth orbit is proportional to : (n = principal quantum number)

Two deuterons undergo nuclear fusion to form a Helium nucleus. Energy released in this process is : (given binding energy per nucleon for deuteron = 1.1 MeV and for helium = 7.0 MeV)

A radioactive nucleus A with a half life T, decays into a nucleus B. At t = 0, there is no nucleus B. At
sometime t, the ratio of the number of B to that of A is 0.3. Then, t is given by :

Some energy levels of a molecule are shown in the figure. The
ratio of the wavelengths r = \({{\lambda _1}}\)/\({{\lambda _2}}\), is given by: