Atoms - Quiz 7

ATOMS QUIZ-7

Dear Readers,

JEE Advanced Physics Syllabus can be referred by the IIT aspirants to get a detailed list of all topics that are important in cracking the entrance examination. JEE Advanced syllabus for Physics has been designed in such a way that it offers very practical and application-based learning to further make it easier for students to understand every concept or topic by correlating it with day-to-day experiences. In comparison to the other two subjects, the syllabus of JEE Advanced for physics is developed in such a way so as to test the deep understanding and application of concepts.

Q1. Figure represents some of the lower energy levels of the hydrogen atom in simplified form If the transition of an electron from E₄ to E₂ were associated with the emission of blue light, which one of the following transitions could be associated with the emission of red light?

•  E₄ to E₁
•  E₃ to E₁
•  E₃ to E₂
•  E₁ to E₃

Solution

(c) For emission of a photon with greater wavelength, energy gap should be less Blue light falls in the Balmer series and it is obtained when the atom makes transition from E₄ to E₃. Red light also falls in the Balmer series and it has a lower frequency compared to blue light. By quantum theory of radiation, the energy change E is proportional to the frequency of electromagnetic radiation f by E=hf. Thus, red light is associated with a smaller energy change from a lower energy level (compared to E₄) to the first excited state E₂. Hence, the only possible transition that result in the emission of red light is the E₃ to E₂ transition

Q2. Magnetic moment due to the motion of the electron in n^th energy of hydrogen atom is proportional to

•  n
•  n⁰
•  n⁵
•  n³

Solution

Q3. Consider a hypothetical annihilation of a stationary electron with a stationary positron. What is the wavelength of the resulting radiation?

•   λ=h/(m₀ c)
•  λ=2h/(m₀ c² )
•  λ=h/(2m₀ c² )
•  None of these

Solution

Q4. A neutron having kinetic energy 5 eV is incident on a hydrogen atom in its ground state. The collision

•  Must be elastic
•  Must be completely inelastic
•  May be partially elastic
•  Information is insufficient

Solution
(a) (a) For a collision of neutron with hydrogen atom in ground state to be inelastic (partial or complete), the minimum KE of striking neutron must be 20.4 eV. [This condition is derived in theory] As the energy of the given incident neutron is less than 2.4 eV, the collision must be elastic

Q5. When an electron accelerated by potential difference U is bombarded on a specific metal, the emitted X-rays spectrum obtained is shown in figure. If the potential difference is reduced to U/3, the correct spectrum is

•  
  
•  
  
•  
  
•  
  

Solution
(b) λ_m will increase to 3λ_m due to decrease in the energy of bombarding electrons. Hence, no characteristic X-rays will be visible, only continuous X-ray will be produced

Q6. The orbital velocity of an electron in the ground state is v. If the electron is excited to energy state -0.54 eV, its orbital velocity will be

•  V_v
•  V_v/3
•  V_v/5
•  v/7

Solution

Q7. If the average life time of an excited state of hydrogen is of the order of 10^(-8) s, then the number of revolutions an electron will make when it is in n=2 state before coming to ground state will be [Take a₀=0.53 Å and all standard data if required]

•  10⁷
•  8×10⁶
•  2×10⁵
•  None of these

Solution

Q8. If an electron in n=3 orbit of hydrogen atom jumps down to n=2 orbit, the amount of energy released and the wavelength of radiation emitted are

•  0.85 eV,6566 Å
•  1.89 eV,1240 Å
•  1.89 eV,6566 Å
•  1.5 eV,6566 Å

Solution

Q9. A proton of mass m moving with a speed v_0 approaches a stationary proton that is free to move. Assume impact parameter to be zero, i.e., head-on collision. How close will the incident proton go to other proton?

•  e³/(πε₀ m² v₀ )
•  e³/(πε₀ mv₀ )
•  e²/(πε₀ mv₀² )
•  None of the above

Solution

Q10. In which of the following systems will the radius of the first orbit (n=1) be minimum?

•  Doubly ionized lithium
•  Singly ionized helium
•  Deuterium atom
• Hydrogen atom

Solution
(a) Radius of first orbit, r∝1/Z. For doubly ionized lithium, Z will be maximum. Hence, for doubly ionized lithium r will be minimum