Resolução exercício

Ana Paula Harter Vaniel
18 Mar 202007:52

Summary

TLDRThis video explains the energy required to remove an electron from a hydrogen atom, starting from its ground state to infinity. It involves calculating the energy change using a formula that incorporates Planck's constant, the speed of light, and the Rydberg constant. The process is demonstrated step by step, with a specific example where the energy is converted from joules to electron volts. The video also touches on calculating the energy for a mole of hydrogen atoms, providing a thorough understanding of atomic energy transitions and the related mathematical concepts.

Takeaways

  • 😀 The exercise is about calculating the energy required to remove an electron from a hydrogen atom, specifically from the n=1 energy level to infinity.
  • 😀 The energy variation formula is introduced: ΔE = h * c * R_H * (1/n_i² - 1/n_f²), where h is Planck's constant, c is the speed of light, R_H is the Rydberg constant, and n_i and n_f are the initial and final energy levels.
  • 😀 The initial energy level is n=1, and the final energy level is considered to be infinity, which makes 1/n_f² equal to zero.
  • 😀 The calculation involves substituting values for Planck's constant (6.626 x 10^-34 J·s), speed of light (3 x 10^8 m/s), and the Rydberg constant (1.097 x 10^7 m^-1) into the equation.
  • 😀 The energy variation for removing an electron from the hydrogen atom is calculated to be approximately 2.2 x 10^-18 joules.
  • 😀 To convert this energy into electron volts (eV), the energy is divided by the conversion factor (1 eV = 1.602 x 10^-19 joules), resulting in 13.70 eV.
  • 😀 This amount of energy (13.70 eV) corresponds to the energy required to remove one electron from a single hydrogen atom.
  • 😀 The process can be extended to calculate the energy for a mole of hydrogen atoms, using Avogadro's number (6.02 x 10^23 atoms/mol).
  • 😀 When calculating for a mole of hydrogen atoms, the energy required is approximately 1312 kJ/mol.
  • 😀 The script also emphasizes that these calculations can be applied to electrons at higher energy levels, such as n=2, n=3, and beyond, not just n=1.

Q & A

  • What is the purpose of the exercise in the video script?

    -The exercise aims to calculate the energy required to remove an electron from the hydrogen atom, starting from the first energy level (n=1) and moving to an infinite energy level.

  • What equation is used to calculate the energy required to remove an electron from a hydrogen atom?

    -The equation used is ΔE = h × c × R∞ × (1/n₁² - 1/n₂²), where ΔE is the energy variation, h is Planck's constant, c is the speed of light, R∞ is the Rydberg constant, and n₁ and n₂ are the initial and final energy levels, respectively.

  • What values are used for the constants in the energy calculation?

    -The values used are: Planck's constant (h) = 6.626 × 10⁻³⁴ J·s, speed of light (c) = 3 × 10⁸ m/s, and the Rydberg constant (R∞) = 1.097 × 10⁷ m⁻¹.

  • Why does 1/n² become zero when n₂ is infinite?

    -When n₂ approaches infinity, the term 1/n₂² approaches zero, meaning the final energy level is considered to be infinitely far from the nucleus, effectively removing the electron from the atom.

  • What is the calculated energy required to remove an electron from a hydrogen atom?

    -The calculated energy required to remove the electron from the hydrogen atom is approximately 2.2 × 10⁻¹⁸ joules.

  • How is the energy in joules converted to electron volts (eV)?

    -To convert joules to electron volts, the energy in joules is divided by the value of 1 electron volt, which is 1.602 × 10⁻¹⁹ joules. For this case, the energy of 2.2 × 10⁻¹⁸ joules corresponds to about 13.7 eV.

  • What does the term 'electron volts' represent in this context?

    -Electron volts (eV) represent a unit of energy commonly used in atomic and particle physics, where 1 eV is the energy gained by an electron moving through a potential difference of 1 volt.

  • How is the energy required to remove an electron from a mole of hydrogen atoms calculated?

    -To calculate the energy required for a mole of hydrogen atoms, the energy calculated for one atom (2.2 × 10⁻¹⁸ joules) is multiplied by Avogadro's constant (6.02 × 10²³ atoms/mol), resulting in an energy of approximately 1.3 × 10⁶ joules per mole.

  • What is the final energy value for one mole of hydrogen atoms in kilojoules?

    -The energy required to remove the electron from one mole of hydrogen atoms is approximately 1.312 × 10³ kilojoules per mole.

  • Can the same method be used to calculate the energy for electrons in higher energy levels?

    -Yes, the same method can be applied to calculate the energy required to remove electrons from higher energy levels, such as n=2, n=3, and so on. The only change is in the values of n₁ and n₂ in the equation.

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Related Tags
Energy CalculationElectron RemovalHydrogen AtomPhysics TutorialEnergy LevelsQuantum PhysicsPlanck's ConstantSpeed of LightRydberg ConstantMole CalculationScientific Formula