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

2018 8 questions

1. Q502018 · 16 Apr 2018 · Shift 1

   The de-Broglie wavelength (${\lambda }_{\text{B}}$) associated with the electron orbiting in the second excited state of hydrogen atom is related to that in the ground state (${\lambda }_{\text{G}}$) by :

   1. A.${\lambda }_{\text{B}}=2{\lambda }_{\text{G}}$
   2. B.${\lambda }_{\text{B}}=3{\lambda }_{\text{G}}$
   3. C.${\lambda }_{\text{B}}={\lambda }_{\text{G}}/2$
   4. D.${\lambda }_{\text{B}}={\lambda }_{\text{G}}/3$
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   Answer: B

2. Q582018 · 16 Apr 2018 · Shift 1

   Both the nucleus and the atom of some element are in their respective first excited states. They get de-excited by emitting photons of wavelengths ${\lambda }_N,{\lambda }_A$ respectively. The ratio $\frac{{\lambda }_N}{{\lambda }_A}$ is closest to :

   1. A.$10^{-6}$
   2. B.10
   3. C.$10^{-10}$
   4. D.$10^{-1}$
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   Answer: A

3. Q592018 · 16 Apr 2018 · Shift 1

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

   1. A.20 years and 5 years, respectively
   2. B.20 years and 10years, respectively
   3. C.5 years and 20 years, respectively
   4. D.10 years and 20 years, respectively
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   Answer: A

4. Q432018 · 15 Apr 2018 · Shift 1

   Two electrons are moving with non-relativistic speed perpendicular to each other. If corresponding de Broglie wavelength are ${\lambda }_1$ and ${\lambda }_2$, their de Broglie wavelength in the frame of reference attached to their center of masses :

   1. A.${\lambda }_{CM}={\lambda }_1={\lambda }_2$
   2. B.${\lambda }_{CM}=\frac{2{\lambda }_1{\lambda }_2}{\sqrt{{\lambda }_1^2+{\lambda }_2^2}}$
   3. C.$\frac{1}{{\lambda }_{CM}}=\frac{1}{{\lambda }_1}+\frac{1}{{\lambda }_2}$
   4. D.${\lambda }_{CM}=\left(\frac{{\lambda }_1+{\lambda }_2}{2}\right)$
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   Answer: B

5. Q582018 · 15 Apr 2018 · Shift 1

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

   1. A.6 liters
   2. B.7 liters
   3. C.4 liters
   4. D.5 liters
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   Answer: D

6. Q542018 · 8 Apr 2018 · Shift 1

   An electron from various excited states of hydrogen atom emit radiation to come to the ground state. Let ${\lambda }_n,{\lambda }_g$ be the de Broglie wavelength of the electron in the $n^{\text{th}}$ state and the ground state respectively. Let ${\Lambda }_n$ be the wavelength of the emitted photon in the transition from the $n^{\text{th}}$ state to the ground state. For large n, (A, B are constants)

   1. A.${\Lambda }_n\approx A+\frac{B}{{\lambda }_n^2}$
   2. B.${\Lambda }_n\approx A+B{\lambda }_n$
   3. C.${\Lambda }_n^2\approx A+B{\lambda }_n^2$
   4. D.${\Lambda }_n^2\approx \lambda$
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   Answer: A

7. Q552018 · 8 Apr 2018 · Shift 1

   If the series limit frequency of the Lyman series is ${\nu }_L$, then the series limit frequency of the Pfund series is:

   1. A.${\nu }_L/25$
   2. B.$25{\nu }_L$
   3. C.$16{\nu }_L$
   4. D.${\nu }_L/16$
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   Answer: A

8. Q562018 · 8 Apr 2018 · Shift 1

   It is found that if a neutron suffers an elastic collinear collision with deuterium at rest, fractional loss of its energy is $p_d$; while for its similar collision with carbon nucleus at rest, fractional loss of energy is $p_c$. The values of $p_d$ and $p_c$ are respectively :

   1. A.(0, 1)
   2. B.(0.89, 0.28)
   3. C.(0.28, 0.89)
   4. D.(0, 0)
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   Answer: B