Dual Nature, Atoms & Nuclei · JEE Main previous year questions

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 ____.

From the statements given below : (A) The angular momentum of an electron in $n^{\text{th}}$ orbit is an integral multiple of $\hslash$. (B) Nuclear forces do not obey inverse square law. (C) Nuclear forces are spin dependent. (D) Nuclear forces are central and charge independent. (E) Stability of nucleus is inversely proportional to the value of packing fraction. Choose the correct answer from the options given below :

1. A.(B), (C), (D), (E) only
2. B.(A), (C), (D), (E) only
3. C.(A), (B), (C), (E) only
4. D.(A), (B), (C), (D) only

Monochromatic light of frequency $6\times 10^{14}\text{ Hz}$ is produced by a laser. The power emitted is $2\times 10^{-3}\text{ W}$. How many photons per second on an average, are emitted by the source ? (Given $\mathrm{h}=6.63\times 10^{-34}\text{ Js}$ )

1. A.$5\times 10^{15}$
2. B.$7\times 10^{16}$
3. C.$6\times 10^{15}$
4. D.$9\times 10^{18}$

When a metal surface is illuminated by light of wavelength $\lambda$, the stopping potential is $8\mathrm{V}$. When the same surface is illuminated by light of wavelength $3\lambda$, stopping potential is $2\mathrm{V}$. The threshold wavelength for this surface is:

1. A.$3\lambda$
2. B.$9\lambda$
3. C.$5\lambda$
4. D.$4.5\lambda$

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 $=3\times 10^{8}m/s$)

In a photoelectric effect experiment a light of frequency 1.5 times the threshold frequency is made to fall on the surface of photosensitive material. Now if the frequency is halved and intensity is doubled, the number of photo electrons emitted will be:

1. A.doubled
2. B.halved
3. C.Zero
4. D.quadrupled

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

1. A.32
2. B.24
3. C.20
4. D.40

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 $A_2=4A_1$, then $\frac{V_2}{V_1}=$ ____.

The work function of a substance is $3.0\text{ eV}$. The longest wavelength of light that can cause the emission of photoelectrons from this substance is approximately;

1. A.$215\text{ nm}$
2. B.$400\text{ nm}$
3. C.$414\text{ nm}$
4. D.$200\text{ nm}$

An electron of hydrogen atom in an excited state is having energy ${\mathrm{E}}_{\mathrm{n}}=-0.85\text{ eV}$. The maximum number of allowed transitions to lower energy level is _________.

The de-Broglie wavelength of an electron is the same as that of a photon. If velocity of electron is $25\%$ of the velocity of light, then the ratio of K.E. of electron and K.E. of photon will be:

1. A.$\frac{1}{4}$
2. B.$\frac{8}{1}$
3. C.$\frac{1}{8}$
4. D.$\frac{1}{1}$

The explosive in a Hydrogen bomb is a mixture of ${}_1{\text{H}}^2,{}_1{\text{H}}^3$ and ${}_3{\text{Li}}^6$ in some condensed form. The chain reaction is given by ${}_3{\text{Li}}^6+{}_0{\text{n}}^1\to {}_2{\text{He}}^4+{}_1{\text{H}}^3$ ${}_1{\text{H}}^2+{}_1{\text{H}}^3\to {}_2{\text{He}}^4+{}_0{\text{n}}^1$ During the explosion the energy released is approximately [Given ; $\text{M(Li)}=6.01690\text{ amu}$, $\text{M}\left({}_1{\text{H}}^2\right)=2.01471\text{ amu}$, $\text{M}\left({}_2{\text{He}}^4\right)=4.00388\text{ amu}$, and $1\text{ amu}=931.5\text{ MeV}$]

1. A.$22.22\text{ MeV}$
2. B.$28.12\text{ MeV}$
3. C.$16.48\text{ MeV}$
4. D.$12.64\text{ MeV}$

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

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 cloud of positive charges with electrons embedded in it, is a special case of Rutherford's model. In the light of the above statements, choose the most appropriate from the options given below

1. A.Both Statement I and Statement II are true
2. B.Statement I is true but Statement II is false
3. C.Statement I is false but Statement II is true
4. D.Both statement I and statement II are false

Two sources of light emit with a power of $200\text{ W}$. The ratio of number of photons of visible light emitted by each source having wavelengths $300\text{ nm}$ and $500\text{ nm}$ respectively, will be :

1. A.$5:3$
2. B.$3:5$
3. C.$1:5$
4. D.$1:3$

Hydrogen atom is bombarded with electrons accelerated through a potential difference of V, which causes excitation of hydrogen atoms. If the experiment is being performed at $\mathrm{T}=0\text{ K}$, the minimum potential difference needed to observe any Balmer series lines in the emission spectra will be $\frac{\alpha }{10}\text{ V}$, where $\alpha =$ _________.

In a nuclear fission process, a high mass nuclide ($A\approx 236$) with binding energy $7.6\text{ MeV/ Nucleon}$ dissociated into middle mass nuclides ($A\approx 118$), having binding energy of $8.6\text{ MeV/Nucleon}$. The energy released in the process would be _____ $\text{MeV}$.

The threshold frequency of a metal with work function $6.63\text{ eV}$ is :

1. A.$16\times 10^{15}\text{ Hz}$
2. B.$16\times 10^{12}\text{ Hz}$
3. C.$1.6\times 10^{15}\text{ Hz}$
4. D.$1.6\times 10^{12}\text{ Hz}$

The electric potential at the surface of an atomic nucleus ($z=50$) of radius $9\times 10^{-13}\text{ cm}$ is _______ $\times 10^6\text{ V}$.

The difference between threshold wavelengths for two metal surfaces A and B having work function ${\varphi }_A=9\text{ eV}$ and ${\varphi }_B=4.5\text{ eV}$ in nm is: { Given, $hc=1242\text{ eV nm}$}

1. A.$264$
2. B.$138$
3. C.$540$
4. D.$276$

$${}_{92}^{238}\mathrm{A}\to {}_{90}^{234}\mathrm{B}+{}_2^4\mathrm{D}+Q$$ In the given nuclear reaction, the approximate amount of energy released will be: [Given, mass of ${}_{92}^{238}\mathrm{A}=238.05079\times 931.5\text{ MeV}/c^2$, mass of ${}_{90}^{234}\mathrm{B}=234.04363\times 931.5\text{ MeV}/c^2$, mass of ${}_2^4\mathrm{D}=4.00260\times 931.5\text{ MeV}/c^2$]

1. A.$2.12\text{ MeV}$
2. B.$4.25\text{ MeV}$
3. C.$3.82\text{ MeV}$
4. D.$5.9\text{ MeV}$

The radius of $2^{\text{nd}}$ orbit of ${\mathrm{He}}^{+}$ of Bohr's model is $r_1$ and that of fourth orbit of ${\mathrm{Be}}^{3+}$ is represented as $r_2$. Now the ratio $\frac{r_2}{r_1}$ is $x:1$. The value of $x$ is ___________.

Given below are two statements: one is labelled as Assertion $\mathbf{A}$ and the other is labelled as Reason $\mathbf{R}$ Assertion A : The binding energy per nucleon is practically independent of the atomic number for nuclei of mass number in the range 30 to 170 . Reason R : Nuclear force is short ranged. In the light of the above statements, choose the correct answer from the options given below

1. A.A is false but $\mathbf{R}$ is true
2. B.A is true but $\mathbf{R}$ is false
3. C.Both $\mathbf{A}$ and $\mathbf{R}$ are true and $\mathbf{R}$ is the correct explanation of $\mathbf{A}$
4. D.Both $\mathbf{A}$ and $\mathbf{R}$ are true but $\mathbf{R}$ is NOT the correct explanation of $\mathbf{A}$

An atom absorbs a photon of wavelength $500\text{ nm}$ and emits another photon of wavelength $600\text{ nm}$. The net energy absorbed by the atom in this process is $n\times 10^{-4}\text{ eV}$. The value of $n$ is ___________. [Assume the atom to be stationary during the absorption and emission process] (Take $h=6.6\times 10^{-34}\text{ Js}$ and $c=3\times 10^8\text{ m/s}$ )

A proton and an $\alpha$-particle are accelerated from rest by $2\text{ V}$ and $4\text{ V}$ potentials, respectively. The ratio of their de-Broglie wavelength is :

1. A.$4:1$
2. B.$2:1$
3. C.$8:1$
4. D.$16:1$