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Discipline: Physics

Question topic: Quantum Mechanics: Introduction

Source: Originais Teachy

Level of difficulty: Medium

(Originais Teachy 2023) - Question Medium of Physics

The Bohr atom was developed by Niels Bohr in 1913, in order to explain the structure of the atom. Bohr's model was based on Max Planck's quantum theory and Balmer-Rydberg's energy law. This theory describes that electrons move in circular orbits at a specific distance from the atom's nucleus, with a defined energy level. What are the two main characteristics of the Bohr atom?
The existence of defined energy levels and the presence of circular electron orbits.
The existence of subatomic particles and the presence of circular electron orbits.
The existence of subatomic particles and the presence of defined energy levels.
The existence of subatomic particles and the presence of orbital particles.
The existence of subatomic particles and the presence of quantum waves.


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Quantum Mechanics: Introduction
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Question 1:


A experimental laboratory is performing measurements on subatomic particles to accurately determine their positions and moments. However, according to Heisenberg's Uncertainty Principle, it is not possible to simultaneously measure the position and momentum of a particle with absolute precision. (a) Suppose a researcher is able to determine the position of an electron with an uncertainty of ∆x = 1.0 × 10^-10 m. Calculate the minimum uncertainty in the measurement of the momentum of this electron, considering the Planck constant h equal to 6.63 × 10^-34 J.s. (b) Based on the momentum uncertainty you found in part (a), calculate the minimum velocity that this electron could have when measured. (c) Discuss the implications of this result in the context of atomic-scale measurements and explain why Heisenberg's Uncertainty Principle is important for understanding the limits of measurements in quantum physics.
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Question 2:


In 1913, Niels Bohr proposed the Bohr atomic model to explain the line spectrum of the hydrogen atom. A hydrogen atom is composed of a single proton and one electron. Suppose you are conducting an experiment in the laboratory and want to investigate the hydrogen atom using the Bohr model. (a) Calculate the kinetic energy of the electron when it is in the ground state (n=1). (b) Determine the radius of the electron's orbit in the ground state according to the Bohr model. (c) If the electron transitions from n=1 to n=2, calculate the amount of energy required for this transition.
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Question 3:


Source: EAM
Question 4:


An experiment was conducted in a laboratory in which two blocks of 1 kg of ice and water, each with different temperatures, are placed in a thermally insulated container. Initially, the ice block is at -20°C and the water, in liquid state, is at 100°C. After some time, we observe that the temperature of the blocks stabilizes at 0°C and the initial ice block completely melts. Knowing that the specific heat of water is 4186 J/(kg·K) and the specific heat of ice is 2090 J/(kg·K), the enthalpy of fusion of ice is 333 kJ/kg and that water is incompressible: a) Calculate the amount of heat exchanged between the ice block and the liquid water for the ice to completely melt and the temperature of the blocks to be in equilibrium. b) Determine the entropy change for each block during the process. c) Considering the system formed by the two blocks and respecting the second law of thermodynamics, verify if the total entropy of the system increased, decreased, or remained constant.
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