Atomic Structure: Bohr's Model

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Questions and Answers

Rutherford's alpha-particle scattering experiment led to what conclusion about the structure of an atom?

  • Neutrons are present in the nucleus.
  • Mass and energy are related.
  • The mass and positive charge are concentrated in the nucleus. (correct)
  • Atoms are electrically neutral.

Which statement is NOT true regarding cathode rays?

  • They possess kinetic energy.
  • They produce mechanical pressure.
  • They are electromagnetic waves. (correct)
  • They produce heat.

The radius of a hydrogen atom in the ground state is 0.53 Å. What is the radius of $Li^{2+}$ in a similar state?

  • 0.265 Å
  • 0.17 Å (correct)
  • 1.06 Å
  • 0.53 Å

The Bohr radius for a hydrogen atom (n=1) is approximately 0.530 Å. What is the radius for the first excited state (n=2)?

<p>2.12 Å (B)</p> Signup and view all the answers

In a hydrogen atom, the energy of the first excited state is -3.4 eV. What is the kinetic energy of the same orbit?

<p>+3.4 eV (D)</p> Signup and view all the answers

The energy of the second Bohr orbit of the hydrogen atom is -328 kJ mol⁻¹. Determine the energy of the fourth Bohr orbit.

<p>-82 kJ mol⁻¹ (C)</p> Signup and view all the answers

In which of the following electronic transitions will minimum energy be absorbed?

<p>n = 4 to n = 5 (D)</p> Signup and view all the answers

According to Rutherford's model, what region of the atom contains nearly all of its mass?

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

One of the drawbacks of Rutherford's model is that it could not explain:

<p>The stability of atoms. (C)</p> Signup and view all the answers

What key assumption is made when applying the Bohr model to atoms or ions?

<p>The atom or ion has only a single electron. (A)</p> Signup and view all the answers

According to Bohr's theory, what causes an electron to emit energy in the form of electromagnetic radiation?

<p>Transitioning from a higher energy level to a lower energy level. (A)</p> Signup and view all the answers

Which of the following statements correctly describes a 'stationary orbit' in Bohr's atomic model?

<p>An orbit where the electron does not lose energy while revolving. (C)</p> Signup and view all the answers

If an electron moves from n=1 to n=3 in a hydrogen atom, how does the potential energy (PE) change?

<p>PE becomes less negative. (A)</p> Signup and view all the answers

What mathematical relationship did Bohr use to quantize the angular momentum of an electron in an atom?

<p>$mvr=nh/2π$ (B)</p> Signup and view all the answers

Which of the following is a major limitation of the Bohr model of the atom?

<p>It fails to explain the spectra of multi-electron atoms. (A)</p> Signup and view all the answers

What is the significance of the term 'Z' when applying the Bohr model to calculate the energy of an electron in a hydrogen-like species?

<p>It represents the atomic number. (A)</p> Signup and view all the answers

How does the velocity of an electron in the Bohr model change as it orbits closer to the nucleus?

<p>Velocity increases. (B)</p> Signup and view all the answers

Which scientist is credited with discovering the atomic nucleus through the gold foil experiment?

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

What type of particles were used in Rutherford's scattering experiment?

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

What aspect of atomic structure did J.J. Thomson's model primarily address?

<p>The presence of electrons (D)</p> Signup and view all the answers

Why is the Bohr model not applicable to multi-electron species?

<p>It doesn't account for electron-electron interactions. (D)</p> Signup and view all the answers

What concept did Bohr introduce to explain the stability of the atom, which was lacking in Rutherford's model?

<p>Quantized energy levels (A)</p> Signup and view all the answers

According to Bohr's postulates, when does an atom emit radiation?

<p>When an electron transitions from a higher to a lower energy orbit. (C)</p> Signup and view all the answers

If 'n' represents the principal quantum number, how does the energy of an electron in a hydrogen atom change as 'n' increases?

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

Which of the following best describes the shape of electron orbits in Bohr's atomic model?

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

In the context of the Bohr model, what happens to the radius of an electron's orbit as the principal quantum number 'n' increases?

<p>The radius increases (B)</p> Signup and view all the answers

What experimental observation led Rutherford to conclude that the atom is mostly empty space?

<p>Most alpha particles passed straight through the gold foil. (C)</p> Signup and view all the answers

Which of the provided options provides the best explanation of why Rutherford's model was ultimately considered incomplete?

<p>It predicted that atoms should emit continuous spectra, not discrete ones. (D)</p> Signup and view all the answers

Flashcards

Rutherford Model

An atomic model where nearly all of the mass and positive charge is concentrated in a small region called the nucleus.

Rutherford Model Drawbacks

Rutherford's model could not explain the stability of atoms or information about electron distribution.

Bohr's Model: Stationary Orbits

Electrons revolve in stationary orbits without losing energy.

Bohr Model of Atom

Bohr's model introduced the concept of stationary orbits to explain atom stability.

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Major Drawback of Bohr Model

e⁻-e⁻ repulsion was missing.

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Bohr Formula Validity

Bohr's formula is valid only for single-electron atoms or ions such as H, He+, and Li2+.

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Rutherford's Conclusion

The mass and the positive charge of an atom are concentrated in the nucleus.

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Cathode Rays

A beam of electron

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Ground state

n=1

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1st excited state

n=2

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Calculate KE

+3.4 eV

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Second Bohr Orbit`s enery

The first excited state energy of hydrogen atom is -328 kJ mol.

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Study Notes

  • The lecture focuses on atomic structure, specifically Bohr's model

Rutherford's Model

  • In Rutherford's model, the atom’s entire mass and positive charge are concentrated in a small region called the nucleus.
  • The approximate size of the nucleus is 10^-15 meters
  • Electrons revolve around the nucleus in circular orbits according to the Rutherford Model

Drawbacks of Rutherford's Model

  • Rutherford's model could not explain the stability of atoms.
  • According to classical electromagnetic theory, electrons should lose energy and spiral into the nucleus
  • The model provided no information about the distribution of electrons

Bohr's Model

  • Bohr's model addresses the limitations of Rutherford's model by explaining the stability of the atom
  • It introduces the concept of stationary orbits: electrons revolve in specific orbits without losing energy
  • Electrons can only occupy certain orbits with fixed energy levels
  • When an electron is revolving in a stationary orbit it will not lose its energy
  • mvr = nh/2π, where m is mass, v is velocity, r is the radius, n is the orbit number, and h is Planck's constant
  • mv²/r = 1/(4πε₀) * (Ze)e / r² which can be expressed as mv²/r = KZe²/r²

Calculations based on Bohr's Model

  • vn = 2.186 x 10^6 m/s * (Z/n), where vn is velocity, Z is atomic number, and n is the principal quantum number
  • rn = 0.529 Å * (n²/Z), where rn is radius, n is the principal quantum number, and Z is the atomic number
  • Potential Energy (PE) = -2 * 13.6 * (Z²/n²) eV
  • Kinetic Energy (KE) = +13.6 * (Z²/n²) eV
  • Total Energy (PE + KE) = -13.6 * (Z²/n²) eV
  • 1 eV = 1.6 x 10^-19 J
  • Shell numbers: K shell corresponds to n=1, L shell to n=2, M shell to n=3, and N shell to n=4

Major Drawbacks of Bohr's Model

  • The model does not account for electron-electron repulsion in multi-electron atoms
  • Bohr's formula is only valid for single-electron atoms or ions.
  • Single electron atom or ions include H, He+, Li+2, Be+3 and Na+10

Additional Information and Formulae

  • Ground state corresponds to n=1
  • First excited state corresponds to n=2
  • Second excited state corresponds to n=3

Example Questions

  • Rutherford's alpha-particle scattering experiments led to the conclusion that the mass and positive charge of an atom are concentrated in the nucleus

  • Which of the following is never true for cathode rays: They are electromagnetic waves, cathode rays are a beam of electrons

  • The radius of the hydrogen atom in the ground state is 0.53 Å. The radius of Li2+ in a similar state is 0.17 Å

  • Bohr radius for the hydrogen atom (n=1) is approximately 0.53 Å. The radius for the first excited state (n = 2) is 2.12 Å

  • In a hydrogen atom, if the energy of the first excited state is -3.4 eV, then the kinetic energy (KE) of the same orbit of the hydrogen atom is +3.4 eV

  • The energy of the second Bohr orbit of the hydrogen atom is -328 kJ mol^-1, therefore, the energy of the fourth Bohr orbit would be -82 kJ mol^-1

  • Minimum energy absorbed in electronic transitions often involves transitions between higher energy levels with smaller gaps

  • In which of the following transitions is minimum energy absorbed: n=4 to n=5

  • Energy level diagram illustration:

  • n=6 has an energy level of -1.51

  • n=3 has an energy level of -3.4 ev

  • n=1 has an energy level of -13.6

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