Nuclei

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. The difference in mass of a nucleus and its constituents is called the mass defect.
Choose the correct answer from the options given below :

\({}_{82}^{290}X\overset{\alpha }{\to }Y\overset{{\mathrm{e}}^{+}}{\to }Z\overset{{\beta }^{-}}{\to }P\overset{{\mathrm{e}}^{-}}{\to }Q\)

In the nuclear emission stated above, the mass number and atomic number of the product Q respectively, are :

[NEET 2024]

If ' f ' denotes the ratio of the number of nuclei decayed \(\left({N}_{d}\right)\) to the number of nuclei at \(t=0\left({\mathrm{N}}_{0}\right)\) then for a collection of radioactive nuclei, the rate of change of ' f ' with respect to time is given as: [ \(\lambda\) is the radioactive decay constant]

[JEE Main 2021, 27 Jul (Shift 1)]

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

[NEET 2023]

A particle of mass \(4 M\) at rest disintegrates into two particles of mass \(M\) and \(3 M\) respectively having non zero velocities. The ratio of de-Broglie wavelength of particle of mass \(M\) to that of mass \(3 M\) will be:

[JEE Main 2021, 25 Jul (Shift 1)]

What happens to the mass number and atomic number of an element when it emits \( \gamma \)-radiation?

Statement 1: For \(30Statement 2: Nuclear force is a long-range force.

(Shift - II Memory Based)

\({}_{92}^{238}A\to {}_{90}^{234}B+{}_{2}^{4}D+Q\)

In the given nuclear reaction, the approximate amount of energy released will be:
[Given, mass of \({}_{92}^{238}A=238.05079\times 931.5\mathrm{MeV}/{\mathrm{c}}^{2}\), mass of \({}_{90}^{234}B=234.04363\times 931.5\mathrm{MeV}/{\mathrm{c}}^{2},\mathrm{m}\) as s of \({}_{2}^{4}D=4.00260\times 931.5\mathrm{MeV}/{\mathrm{c}}^{2}\) ]

[JEE Main 2023, 13 Apr (Shift 1)]

The mass of proton, neutron and helium nucleus are respectively \(1.0073\mathrm{u},1.0087\mathrm{u}\) and \(4.0015\mathrm{u}\). The binding energy of helium nucleus is:

[JEE Main 2023, 1 Feb (Shift 1)]

There are \({10}^{10}\) radioactive nuclei in a given radioactive element, Its half-life time is 1 minute. How many nuclei will remain after 30 seconds? \((\sqrt{2}=1.414)\)

[JEE Main 2021, 27 Aug (Shift 1)]

A nucleus of mass \( M \) emits \( \gamma \)-ray photon of frequency \( v \) . The loss of internal energy by the nucleus is [Take \( c \) as the speed of electromagnetic wave]

[JEE Main 2021, 20 Jul (Shift 1)]

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

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

[JEE Main 2023, 8 Apr (Shift 2)]

The half life of a radioactive nuclide is 100 hours . The fraction of original activity that will remain after 150 hours would be

A radioactive material decays by simultaneous emissions of two particles with half lives of 1400 years and 700 years respectively. What will be the time after which one third of the material remains? (Take \(\ln 3=1.1\) )

[JEE Main 2021, 20 Jul (Shift 1)]

A nucleus with mass number 240 breaks into two fragments each of mass number 120 , the binding energy per nucleon of unfragmented nuclei is \( 7.6 \mathrm{MeV} \) while that of fragments is \( 8.5 \mathrm{MeV} \). The total gain in the Binding Energy in the process is:

Consider the following statements:
(A) Atoms of each element emit characteristics spectrum.
(B) According to Bohr's Postulate, an electron in a hydrogen atom, revolves in a certain stationary orbit.
(C) The density of nuclear matter depends on the size of the nucleus.
(D) A free neutron is stable but a free proton decay is possible.
(E) Radioactivity is an indication of the instability of nuclei.

Choose the correct answer from the options given below:

The energy equivalent of \( 0.5 \mathrm{~g} \) of a substance is:

[NEET 2020]

A nucleus with mass number 240 breaks into two fragments each of mass number 120 , the binding energy per nucleon of unfragmented nuclei is \( 7.6 \mathrm{MeV} \) while that of fragments is \( 8.5 \mathrm{MeV} \). The total gain in the Binding Energy in the process is:

[NEET 2021]