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

If ${\lambda }_1$ and ${\lambda }_2$ are the wavelengths of the third member of Lyman and first member of the Paschen series respectively, then the value of ${\lambda }_1:{\lambda }_2$ is :

1. A.7 : 135
2. B.7 : 108
3. C.1 : 9
4. D.1 : 3

The recoil speed of a hydrogen atom after it emits a photon in going from n = 5 state to n = 1 state will be :

1. A.4.34 m/s
2. B.2.19 m/s
3. C.3.25 m/s
4. D.4.17 m/s

A radioactive sample is undergoing $\alpha$ decay. At any time $t_1$, its activity is A and another time $t_2$, the activity is $\frac{A}{5}$. What is the average life time for the sample?

1. A.$\frac{\ln 5}{t_2-t_1}$
2. B.$\frac{\ln (t_2+t_1)}{2}$
3. C.$\frac{t_1-t_2}{\ln 5}$
4. D.$\frac{t_2-t_1}{\ln 5}$

Two streams of photons, possessing energies equal to twice and ten times the work function of metal are incident on the metal surface successively. The value of ratio of maximum velocities of the photoelectrons emitted in the two respective cases is x : y. The value of x is ___________.

An electron of mass $m_e$ and a proton of mass $m_p=1836m_e$ are moving with the same speed. The ratio of their de Broglie wavelength $\frac{{\lambda }_{electron}}{{\lambda }_{proton}}$ will be :

1. A.1
2. B.1836
3. C.$\frac{1}{1836}$
4. D.918

The stopping potential for electrons emitted from a photosensitive surface illuminated by light of wavelength 491 nm is 0.710 V. When the incident wavelength is changed to a new value, the stopping potential is 1.43 V. The new wavelength is :

1. A.400 nm
2. B.329 nm
3. C.309 nm
4. D.382 nm

The wavelength of an X-ray beam is $10\text{A˚}$. The mass of a fictitious particle having the same energy as that of the X-ray photons is $\frac{x}{3}h\text{ kg}$. The value of x is ______ . (h = Planck's constant)

An electron, a doubly ionized helium ion ($\mathrm{H}{\mathrm{e}}^{++}$) and a proton are having the same kinetic energy. The relation between their respective de-Broglie wavelengths ${\lambda }_e$, ${\lambda }_{\mathrm{H}{\mathrm{e}}^{++}}$ and ${\lambda }_p$ is :

1. A.${\lambda }_e>{\lambda }_{\mathrm{H}{\mathrm{e}}^{++}}>{\lambda }_p$
2. B.${\lambda }_e<{\lambda }_p<{\lambda }_{\mathrm{H}{\mathrm{e}}^{++}}$
3. C.${\lambda }_e>{\lambda }_p>{\lambda }_{\mathrm{H}{\mathrm{e}}^{++}}$
4. D.${\lambda }_e<{\lambda }_{\mathrm{H}{\mathrm{e}}^{++}}={\lambda }_p$

You are given that Mass of ${}_3^7\mathrm{Li}=7.0160\text{u}$, Mass of ${}_2^4\mathrm{He}=4.0026\text{u}$ and Mass of ${}_1^1\mathrm{H}=1.0079\text{u}$. When $20\text{ g}$ of ${}_3^7\mathrm{Li}$ is converted into ${}_2^4\mathrm{He}$ by proton capture, the energy liberated, (in $\mathrm{kWh}$), is : $[\text{Mass of nucleon}=1\mathrm{GeV}/c^2]$

1. A.$6.82\times 10^5$
2. B.$4.5\times 10^5$
3. C.$8\times 10^6$
4. D.$1.33\times 10^6$

Assuming the nitrogen molecule is moving with r.m.s. velocity at $400\text{ K}$, the de-Broglie wavelength of nitrogen molecule is close to : (Given : nitrogen molecule weight : $4.64\times 10^{-26}\text{ kg}$, Boltzmann constant: $1.38\times 10^{-23}J/K$, Planck constant : $6.63\times 10^{-34}J.s$)

1. A.$0.44\text{A˚}$
2. B.$0.34\text{A˚}$
3. C.$0.20\text{A˚}$
4. D.$0.24\text{A˚}$

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

1. A.$\frac{3}{4}$
2. B.$\frac{4}{5}$
3. C.$\frac{3}{5}$
4. D.$\frac{7}{8}$

Two sources of light emit X-rays of wavelength 1 nm and visible light of wavelength 500 nm, respectively. Both the sources emit light of the same power 200 W. The ratio of the number density of photons of X-rays to the number density of photons of the visible light of the given wavelengths is :

1. A.$\frac{1}{500}$
2. B.500
3. C.250
4. D.$\frac{1}{250}$

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

1. A.$10^{24}\mathrm{kg}{\mathrm{m}}^{-3}$
2. B.$10^{10}\mathrm{kg}{\mathrm{m}}^{-3}$
3. C.$10^{17}\mathrm{kg}{\mathrm{m}}^{-3}$
4. D.$10^3\mathrm{kg}{\mathrm{m}}^{-3}$

In a reactor, 2 kg of ${}_{92}{\mathrm{U}}^{235}$ fuel is fully used up in 30 days. The energy released per fission is 200 MeV. Given that the Avogadro number, $\mathrm{N}=6.023\times 10^{26}$ per kilo mole and $1\text{ eV}=1.6\times 10^{-19}\text{ J}$. The power output of the reactor is close to

1. A.125 MW
2. B.60 MW
3. C.54 MW
4. D.35 MW

When radiation of wavelength $\lambda$ is used to illuminate a metallic surface, the stopping potential is $V$. When the same surface is illuminated with radiation of wavelength $3\lambda$, the stopping potential is $\frac{V}{4}$. If the threshold wavelength for the metallic surface is $n\lambda$ then value of $n$ will be ____.

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

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

A particle is moving 5 times as fast as an electron. The ratio of the de-Broglie wavelength of the particle to that of the electron is $1.878\times 10^{-4}$. The mass of the particle is close to

1. A.$1.2\times 10^{-28}\mathrm{kg}$
2. B.$9.1\times 10^{-31}\mathrm{kg}$
3. C.$4.8\times 10^{-27}\mathrm{kg}$
4. D.$9.7\times 10^{-28}\mathrm{kg}$

A particle moving with kinetic energy E has de Broglie wavelength $\lambda$. If energy $\Delta \mathrm{E}$ is added to its energy, the wavelength become $\lambda /2$. Value of $\Delta \mathrm{E}$, is :

1. A.E
2. B.3E
3. C.2E
4. D.4E

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 ?

1. A.35.8 nm
2. B.11.4 nm
3. C.8.6 nm
4. D.24.2 nm

When photon of energy 4.0 eV strikes the surface of a metal A, the ejected photoelectrons have maximum kinetic energy ${\mathrm{T}}_{\mathrm{A}}$ eV and de-Broglie wavelength ${\lambda }_A$. The maximum kinetic energy of photoelectrons liberated from another metal B by photon of energy 4.50 eV is ${\mathrm{T}}_{\mathrm{B}}=({\mathrm{T}}_{\mathrm{A}}-1.5)\text{ eV}$. If the de-Broglie wavelength of these photoelectrons ${\lambda }_B=2{\lambda }_A$, then the work function of metal B is :

1. A.1.5eV
2. B.4eV
3. C.2eV
4. D.3eV

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 $1.6\times 10^{-16}\text{ s}$. The frequency of revolution of the electron in its first excited state (in ${\text{s}}^{-1}$) is :

1. A.$5.6\times 10^{12}$
2. B.$1.6\times 10^{14}$
3. C.$7.8\times 10^{14}$
4. D.$6.2\times 10^{15}$

A beam of electromagnetic radiation of intensity $6.4\times 10^{-5}W/c{\mathrm{m}}^2$ is comprised of wavelength, $\lambda =310\mathrm{nm}$. It falls normally on a metal (work function $\varphi =2\mathrm{eV}$) of surface area of $1\mathrm{c}{\mathrm{m}}^2$. If one in $10^3$ photons ejects an electron, total number of electrons ejected in $1\mathrm{s}$ is $10^{\mathrm{x}}$. ($\mathrm{hc}=1240\mathrm{eVnm}$, $1\mathrm{eV}=1.6\times 10^{-19}\mathrm{J}$), then x is ____.

An electron (of mass m) and a photon have the same energy E in the range of a few eV. The ratio of the de-Broglie wavelength associated with the electron and the wavelength of the photon is (c = speed of light in vaccum)

1. A.$\frac{1}{c}{\left(\frac{2E}{m}\right)}^{\frac{1}{2}}$
2. B.$\frac{1}{c}{\left(\frac{E}{2m}\right)}^{\frac{1}{2}}$
3. C.${\left(\frac{E}{2m}\right)}^{\frac{1}{2}}$
4. D.$c(2mE{)}^{\frac{1}{2}}$

The activity of a radioactive sample falls from $700{\text{ s}}^{-1}$ to $500{\text{ s}}^{-1}$ in 30 minutes. Its half life is close to:

1. A.62 min
2. B.66 min
3. C.72 min
4. D.52 min