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

2019 23 questions

1. Q362019 · 12 Apr 2019 · Shift 1
   
   1. A.$1.95\text{ eV}$
   2. B.$2.12\text{ eV}$
   3. C.$1.82\text{ eV}$
   4. D.$1.66\text{ eV}$
   Show answer

   Answer: D

2. Q572019 · 12 Apr 2019 · Shift 1

   An excited ${\text{He}}^{+}$ 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 $\lambda$, energy $E=\frac{1240\text{ eV}}{\lambda (\text{in nm})}$) :

   1. A.$n=4$
   2. B.$n=7$
   3. C.$n=5$
   4. D.$n=6$
   Show answer

   Answer: C

3. Q392019 · 12 Apr 2019 · Shift 2

   Consider an electron in a hydrogen atom revolving in its second excited state (having radius $4.65\text{ A˚}$). The de-Broglie wavelength of this electron is :

   1. A.$6.6\text{ A˚}$
   2. B.$3.5\text{ A˚}$
   3. C.$9.7\text{ A˚}$
   4. D.$12.9\text{ A˚}$
   Show answer

   Answer: C

4. Q402019 · 12 Apr 2019 · Shift 2

   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, $\frac{{\lambda }_1}{{\lambda }_2}$, of the photons emitted in this process is :

   1. A.$\frac{22}{5}$
   2. B.$\frac{7}{5}$
   3. C.$\frac{9}{7}$
   4. D.$\frac{20}{7}$
   Show answer

   Answer: D

5. Q602019 · 12 Apr 2019 · Shift 2

   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 :

   1. A.9 : 8
   2. B.1 : 8
   3. C.8 : 1
   4. D.3 : 8
   Show answer

   Answer: A

6. Q462019 · 10 Apr 2019 · Shift 1

   In a photoelectric effect experiment the threshold wavelength of the light is 380 nm. If the wavelentgh of incident light is 260 nm, the maximum kinetic energy of emitted electrons will be: Given E (in eV) = 1237/$\lambda$ (in nm)

   1. A.4.5 eV
   2. B.15.1 eV
   3. C.3.0 eV
   4. D.1.5 eV
   Show answer

   Answer: D

7. Q582019 · 10 Apr 2019 · Shift 1

   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 :

   1. A.$1/9\lambda$
   2. B.$11/10\lambda$
   3. C.$1/10\lambda$
   4. D.$1/11\lambda$
   Show answer

   Answer: A

8. Q452019 · 10 Apr 2019 · Shift 2

   In $\mathrm{L}{\mathrm{i}}^{++}$, 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 are observed. What is the value of $\lambda$? (Given : $\mathrm{H}=6.63\times 10^{-34}\mathrm{Js};\mathrm{c}=3\times 10^8\mathrm{m}{\mathrm{s}}^{-1}$)

   1. A.10.8 nm
   2. B.12.3 nm
   3. C.9.4 nm
   4. D.11.4 nm
   Show answer

   Answer: A

9. Q562019 · 10 Apr 2019 · Shift 2

   A 2 mW laser operates at wavelength of 500 nm. The number of photons that will be emitted per second is : [Given Planck's constant $h=6.6\times 10^{-34}\mathrm{Js}$, speed of light $c=3.0\times 10^{8}m/s$]

   1. A.$5\times 10^{15}$
   2. B.$1.5\times 10^{16}$
   3. C.$1\times 10^{16}$
   4. D.$2\times 10^{16}$
   Show answer

   Answer: A

10. Q592019 · 10 Apr 2019 · Shift 2

    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 ${\left(\frac{1}{e}\right)}^2$ will be :

    1. A.$\frac{2}{\lambda }$
    2. B.$\frac{1}{4\lambda }$
    3. C.$\frac{1}{2\lambda }$
    4. D.$\frac{1}{\lambda }$
    Show answer

    Answer: C

11. Q542019 · 9 Apr 2019 · Shift 1

    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 :

    1. A.642.7 nm
    2. B.488.9 nm
    3. C.889.2 nm
    4. D.388.9 nm
    Show answer

    Answer: B

12. Q392019 · 9 Apr 2019 · Shift 2

    A particle 'P' is formed due to a completely inelastic collision of particles 'x' and 'y' having de-Broglie wavelengths '${\lambda }_x$' and '${\lambda }_y$' respectively. If x and y were moving in opposite directions, then the de-Broglie wavelength of 'P' is :-

    1. A.${\lambda }_x-{\lambda }_y$
    2. B.$\frac{{\lambda }_x{\lambda }_y}{|{\lambda }_x-{\lambda }_y|}$
    3. C.${\lambda }_x+{\lambda }_y$
    4. D.$\frac{{\lambda }_x{\lambda }_y}{{\lambda }_x+{\lambda }_y}$
    Show answer

    Answer: B

13. Q532019 · 9 Apr 2019 · Shift 2

    A $\mathrm{H}{\mathrm{e}}^{+}$ ion is in its first excited state. Its ionization energy is :-

    1. A.$13.60\mathrm{eV}$
    2. B.$6.04\mathrm{eV}$
    3. C.$48.36\mathrm{eV}$
    4. D.$54.40\mathrm{eV}$
    Show answer

    Answer: A

14. Q522019 · 8 Apr 2019 · Shift 2

    A nucleus A, with a finite de-broglie wavelength ${\lambda }_A$, undergoes spontaneous fission into two nuclei B and C of equal mass. B flies in the same direction as that of A, while C flies in the opposite direction with a velocity equal to half of that of B. The de-Broglie wavelengths ${\lambda }_B$ and ${\lambda }_C$ of B and C are respectively :

    1. A.${\lambda }_A,2{\lambda }_A$
    2. B.$2{\lambda }_A,{\lambda }_A$
    3. C.${\lambda }_A,{\lambda }_A/2$
    4. D.${\lambda }_A/2,{\lambda }_A$
    Show answer

    Answer: D

15. Q592019 · 8 Apr 2019 · Shift 2

    The ratio of mass densities of nuclei of ${}^{40}\mathrm{Ca}$ and ${}^{16}\mathrm{O}$ is close to :-

    1. A.1
    2. B.5
    3. C.0.1
    4. D.2
    Show answer

    Answer: A

16. Q352019 · 12 Jan 2019 · Shift 1

    A particle A of mass 'm' and charge 'q' is accelerated by a potential difference of 50 V. Another particle B of mass '4 m' and charge 'q' is accelerated by a potential difference of 2500 V. The ratio of de-Broglie wavelengths $\frac{{\lambda }_A}{{\lambda }_B}$ is close to :

    1. A.4.47
    2. B.10.00
    3. C.14.14
    4. D.0.07
    Show answer

    Answer: C

17. Q582019 · 12 Jan 2019 · Shift 1

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

    1. A.$r_n\propto \sqrt{n},E_n\propto n$
    2. B.$r_n\propto \sqrt{n},E_n\propto \frac{1}{n}$
    3. C.$r_n\propto n,E_n\propto n$
    4. D.$r_n\propto n^2,E_n\propto \frac{1}{n^2}$
    Show answer

    Answer: A

18. Q412019 · 12 Jan 2019 · Shift 2

    In a Frank-Hertz experiment, an electron of energy 5.6 eV passes through mercury vapour and emerges with an energy 0.7 eV. The minimum wavelength of photons emitted by mercury atoms is close to :

    1. A.2020 nm
    2. B.250 nm
    3. C.1700 nm
    4. D.220 nm
    Show answer

    Answer: B

19. Q432019 · 12 Jan 2019 · Shift 2

    When a certain photosensitive surface is illuminated with monochromatic light of frequency v, the stopping potential for the current is $-V_0/2$. When the surface is illuminated by monochromatic light of frequency v/2, the stopping potential is $-V_0$. The threshold frequency for photoelectric emission is :

    1. A.$2v$
    2. B.$\frac{4}{3}v$
    3. C.$\frac{3v}{2}$
    4. D.$\frac{5v}{3}$
    Show answer

    Answer: C

20. Q592019 · 12 Jan 2019 · Shift 2

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

    1. A.A = 208; Z = 80
    2. B.A = 208; Z = 82
    3. C.A = 200; Z = 81
    4. D.A = 202; Z = 80
    Show answer

    Answer: B

21. Q372019 · 11 Jan 2019 · Shift 2

    In a photoelectric experiment, the wavelength of the light incident on a metal is changed from $300\text{ nm}$ to $400\text{ nm}$. The decrease in the stopping potential is close to: ($\frac{hc}{e}=1240\text{ nm eV}$)

    1. A.$0.5\text{ V}$
    2. B.$1.0\text{ V}$
    3. C.$2.0\text{ V}$
    4. D.$1.5\text{ V}$
    Show answer

    Answer: B

22. Q402019 · 9 Jan 2019 · Shift 1

    Surface of certain metal is first illuminated with light of wavelength ${\lambda }_1=350\text{ nm}$ and then, by light of wavelength ${\lambda }_2=540\text{ nm}$. It is found that the maximum speed of the photo electrons in the two cases differ by a factor of 2. The work function of the metal (in eV) is close to : $(\text{Energy of photon}=\frac{1240}{\lambda (innm)}\text{eV})$

    1. A.1.8
    2. B.2.5
    3. C.5.6
    4. D.1.4
    Show answer

    Answer: A

23. Q602019 · 9 Jan 2019 · Shift 1

    A sample of radioactive material A, that has an activity of $10\text{ mCi}(1\text{ Ci}=3.7\times 10^{10}\text{ decays/s})$, has twice the number of nuclei as another sample of a different radioactive materail B which has an activity of $20\text{ mCi}$. The correct choices for half-lives of A and B would then be respectively :

    1. A.5 days and 10 days
    2. B.10 days and 40 days
    3. C.20 days and 5 days
    4. D.20 days and 10 days
    Show answer

    Answer: C