JEE Advanced 2024: Atomic Structure and Spectroscopy

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Questions and Answers

What is the ratio of the maximum to the minimum photocurrent that can be passed through the circuit?

  • 9 : 5
  • 5 : 4
  • 9 : 2 (correct)
  • 9 : 4

What is the minimum possible wavelength of the photoelectron?

  • 480Å
  • 30Å
  • 120Å (correct)
  • 680Å

What is the value of Z in the given equation?

  • 2
  • 5
  • 3 (correct)
  • 4

What is the value of the radial node in the given equation?

<p>2s (C)</p> Signup and view all the answers

What is the minimum photocurrent that must be passed through the circuit?

<p>0.64 A (A)</p> Signup and view all the answers

What is the circumference of the second orbit of an atom or ion having a single electron?

<p>4 nm (D)</p> Signup and view all the answers

What is the energy of the first photon emitted when the atom transitions from the higher excited state to the first excited state?

<p>10.20 eV (A)</p> Signup and view all the answers

What is the angular node of the 2p orbital in the hydrogen atom?

<p>1 (A)</p> Signup and view all the answers

What is the energy of the photon emitted when the electron moves from the (n + 1) to the ground state?

<p>122.74 eV (C)</p> Signup and view all the answers

What is the region of the electromagnetic spectrum where the Lyman series is observed?

<p>Ultraviolet region (A)</p> Signup and view all the answers

What is the radial node of the 2s orbital in the hydrogen atom?

<p>0 (C)</p> Signup and view all the answers

What happens to the energy of an electron accelerated by a potential difference of 5.0 V when it collides with a Hg atom?

<p>It is converted into light (B)</p> Signup and view all the answers

What is the energy of the second photon emitted when the atom transitions from the higher excited state to the first excited state?

<p>17.00 eV (D)</p> Signup and view all the answers

If a ruby laser produces 0.36 J of energy per pulse, what can be said about the number of photons produced in each pulse?

<p>It is directly proportional to the energy per pulse (A)</p> Signup and view all the answers

What is the effect of halving the intensity of light on the maximum kinetic energy of electrons emitted by a metal surface?

<p>The maximum kinetic energy remains the same (D)</p> Signup and view all the answers

What is the relationship between the radius of the second orbit of a H-atom and that of a He+ ion?

<p>The radius of the second orbit of a H-atom is equal to that of a He+ ion (B)</p> Signup and view all the answers

When an electron jumps from the second orbit to the fourth orbit in a H-atom, what happens to its distance from the nucleus?

<p>It increases by 2.116 Å (A)</p> Signup and view all the answers

What is the wavelength of the light emitted by a Hg-atom when an electron accelerated by a potential difference of 5.0 V collides with it?

<p>248 nm (C)</p> Signup and view all the answers

What is the kinetic energy of an electron in the second Bohr orbit of a hydrogen atom?

<p>h² / (16π² mao²) (B)</p> Signup and view all the answers

What is the radius of the first orbit of a D-atom?

<p>exactly 0.529 Å (B)</p> Signup and view all the answers

What is the energy of an electron in the first Bohr's orbit of an H-atom?

<p>–13.6 eV (A)</p> Signup and view all the answers

Which of the following statements is correct about the Bohr's model of a hydrogen atom?

<p>The kinetic energy of electron in the n = 2 orbit is less than that in the n = 1 orbit (A)</p> Signup and view all the answers

What happens to the kinetic energy of an electron when it jumps from the fourth orbit to the second orbit in a Be³⁺ ion?

<p>it increases (A)</p> Signup and view all the answers

For which orbit in a He⁺ ion is the circumference 26.5 Å?

<p>16 (A)</p> Signup and view all the answers

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Study Notes

Atomic Structure

  • Centripetal force of an electron in the n = 2 orbit is more than that in the n = 1 orbit.

Photocurrent

  • Three laser guns with powers 2, 3, and 5 W are used to produce photocurrent from a metal plate.
  • The number of photons emitted by the laser guns are 4 × 10^18, 5 × 10^18, and 9 × 10^18 per second.
  • The metal plate has a threshold energy of 4.5 × 10^-19 J.

Wavelength of Photoelectron

  • Minimum possible wavelength of a photoelectron is 680Å or 30Å.

Hydrogen-Like Atom

  • A hydrogen-like atom (atomic number Z) is in a higher excited state of quantum number n.
  • The excited atom can make a transition to the first excited state by successively emitting two photons of energies 10.20 and 17.00 eV, respectively.
  • Alternatively, the atom from the same excited state can make a transition to the second excited state by successively emitting two photons of energies 4.25 and 5.95 eV, respectively.

Schrödinger Wave Equation

  • The Schrödinger wave equation for a hydrogen atom is Ψ2s = (1/2) (4√2π/a0) (2 - r0/a0) e^(-r/a0).

Matrices

  • Match the columns: Orbitals (2s, 1s, 2p, 3p) with Nodal properties (Radial node = 0, Angular node = 1, Radial node = 1, Angular node = 0).

Hydrogen Atom Spectrum

  • Match Column I with Column II: Lyman series (UV region), Balmer series (Visible region), Paschen series (IR region), Brackett series (IR region).

Atomic Radius

  • The radius of the second orbit of an H-atom is equal to the radius of the second orbit of a He+ ion.
  • The radius of the first orbit of an H-atom is 0.529 Å.
  • The radius of the first orbit of a D-atom is slightly less than 0.529 Å.

Electron Energy

  • The energy of an electron in the first Bohr's orbit of an H-atom is -13.6 eV.
  • Possible energy values of the excited state(s) for electrons in Bohr's orbits to hydrogen are -3.4 eV, -10.2 eV, -1.51 eV, and -0.85 eV.

Bohr's Model

  • The acceleration of the electron in the n = 2 orbit is more than that in the n = 1 orbit.
  • The angular momentum of the electron in the n = 2 orbit is more than that in the n = 1 orbit.
  • The kinetic energy of an electron in the n = 2 orbit is less than that in the n = 1 orbit.

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