JEE Atoms and Nuclei PYQs With Video Solutions PDF

A particle of mass $$200\,\text{MeV c}^{-2}$$ 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 $$\frac{N}{4}$$. The value of $$N$$ is: (Given the mass of the hydrogen atom to be $$1\,\text{GeV c}^{-2}$$)........

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

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 ($$h = 6.62 \times 10^{-34}$$ J s)

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 $$n^{th}$$ orbit is proportional to: ($$n$$ = principal quantum number)

In the given figure, the energy levels of hydrogen atom have been shown along with some transitions marked A, B, C, D and E. The transitions A, B and C respectively represent

A beam of monochromatic light is used to excite the electron in $$Li^{++}$$ from the first orbit to the third orbit. The wavelength of monochromatic light is found to be $$x \times 10^{-10}$$ m. The value of $$x$$ is ______.
[Given $$hc = 1242$$ eV nm]

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).

Assuming the experimental mass of $$^{12}_{6}C$$ as 12 u, The mass defect of $${}^{12}\text{C}$$ atom is (in MeV/$$c^2$$) :
(Mass of proton  = 1.00727 u, mass of neutron = 1.00866 u, 1 u = 931.5$$ $$MeV/$$c^2$$ and c is the speed of the light in vacuum).

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

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

When a metallic surface is illuminated with radiation of wavelength $$\lambda$$, the stopping potential for the photoelectric current is $$V_0$$. If the same surface is illuminated with radiation of wavelength $$2\lambda$$, the stopping potential becomes $$\frac{V_0}{4}$$. The threshold wavelength ($$\lambda_{th}$$) for this metallic surface is:

For a nucleus $$^A_Z X$$ having mass number A and atomic number Z
A. The surface energy per nucleon $$(b_s) = -a_1 A^{2/3}$$.
B. The Coulomb contribution to the binding energy $$b_c = -a_2 \dfrac{Z(Z-1)}{A^{1/3}}$$.
C. The volume energy $$b_v = a_3 A$$
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:

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

The half life period of a radioactive element $$x$$ is same as the mean life time of another radioactive element $$y$$. Initially they have the same number of atoms. Then:

Imagine that a reactor converts all the given mass into energy and that it operates at a power level of $$10^9$$ Watt. The mass of the fuel consumed per hour, in the reactor, will be: (velocity of light, $$c$$ is $$3 \times 10^8$$ m s$$^{-1}$$)

A radioactive nucleus $$A$$ with a half-life $$T$$, decays into a nucleus $$B$$. At $$t = 0$$, there is no nucleus $$B$$. At some time $$t$$, the ratio of the number of $$B$$ to that of $$A$$ is 0.3. Then, $$t$$ is given by: (Consider $$\log_{e} x = \log x$$)

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

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

A diatomic gas ($$\gamma = 1.4$$) does 100 J of work in an isobaric expansion. The heat given to the gas is :

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:

Muon ($$\mu^{-1}$$) is negatively charged (|q| = |e|) with a mass m$$_\mu$$ = 200 m$$_e$$, where m$$_e$$ is the mass of the electron and e is the electronic charge. If $$\mu^{-1}$$ is bound to a proton to form a hydrogen like atom, identify the correct statements:
(A) Radius of the muonic orbit is 200 times smaller than that of the electron
(B) The speed of the $$\mu^{-1}$$ in the nth orbit is $$\frac{1}{200}$$ times that of the electron in the nth orbit
(C) The ionization energy of muonic atom is 200 times more than that of an hydrogen atom
(D) The momentum of the muon in the nth orbit is 200 times more than that of the electron

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:

A solution containing active cobalt $$^{60}_{27}$$Co having an activity of 0.8 $$\mu$$Ci and decay constant $$\lambda$$ is injected in an animal's body. If 1 cm$$^3$$ blood is drawn from the animal's body after 10 h of injection, the activity found was 300 decays per minute.What is the volume of blood that is flowing in the body? [1 Ci = $$3.7 \times 10^{10}$$ dps (decays per second) and at $$t = 10hrs^{- \lambda t}$$ = 0.84]

The de-Broglie wavelength ($$\lambda_B$$) associated with the electron orbiting in the second excited state of hydrogen atom is related to that in the ground state ($$\lambda_G$$) by:

At some instant, a radioactive sample S$$_1$$ having an activity 5$$\mu$$Ci has twice the number of nuclei as another sample S$$_2$$ which has an activity of 10$$\mu$$Ci. The half lives of S$$_1$$ and S$$_2$$ are:

An electron in a hydrogen atom undergoes a transition from an excited state with principal quantum number $$n_2$$ to the ground state ($$n_1 = 1$$). If the wavelength of the emitted photon is equal to $$\frac{4}{3R}$$, where $$R$$ is the Rydberg constant, then the value of the principal quantum number $$n_2$$ of the initial excited state is:

The minimum kinetic energy needed by an alpha particle to cause the nuclear reaction $$^{16}_7N + ^4_2He \to ^1_1H + ^{19}_8O$$ in a laboratory frame is $$n$$ (in MeV). Assume that $$^{16}_7N$$ is at rest in the laboratory frame. The masses of $$^{16}_7N$$, $$^4_2He$$, $$^1_1H$$ and $$^{19}_8O$$ can be taken to be 16.006 $$u$$, 4.003 $$u$$, 1.008 $$u$$ and 19.003 $$u$$, respectively, where 1 $$u$$ = 930 MeV$$c^{-2}$$. The value of $$n$$ is ______.

A common example of alpha decay is $$^{238}_{92}$$U $$\to ^{234}_{90}$$Th $$+ _2$$He$$^4 + Q$$
Given:
$$^{238}_{92}$$U $$= 238.05060$$ u
$$^{234}_{90}$$Th $$= 234.04360$$ u
$$^4_2$$He $$= 4.00260$$ u and $$1$$u $$= 931.5$$ $$\frac{\text{MeV}}{c^2}$$
The energy released $$(Q)$$ during the alpha decay of $$^{238}_{92}$$U is _____ MeV.

The radius R of a nucleus of mass number A can be estimated by the formula $$R = (1.3 \times 10^{-15})A^{1/3}$$ m. It follows that the mass density of n nucleus is of the order of: $$(M_{prot} \cong M_{neut} \simeq 1.67 \times 10^{-27}$$ kg)

A radioactive sample has a half-life of $$10\text{ days}$$. If the initial activity of the sample is $$A_0$$, the time required for the activity to reduce to $$\frac{A_0}{8}$$ is: