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What happens when an electron falls from a higher energy level to a lower one?
What happens when an electron falls from a higher energy level to a lower one?
According to Planck’s formula, what does the variable 'E' represent?
According to Planck’s formula, what does the variable 'E' represent?
What is the relationship between the energy levels of an electron in a hydrogen atom and the value of n?
What is the relationship between the energy levels of an electron in a hydrogen atom and the value of n?
What provides the centripetal force necessary to hold the electron in orbit around the nucleus?
What provides the centripetal force necessary to hold the electron in orbit around the nucleus?
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In the equation $\frac{nh}{2\pi} = mv_n r_n$, what does 'n' represent?
In the equation $\frac{nh}{2\pi} = mv_n r_n$, what does 'n' represent?
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What is the formula for the radius of a stable orbit in the nth state of an atom?
What is the formula for the radius of a stable orbit in the nth state of an atom?
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What is the energy of an electron in the n=5 state of a hydrogen atom?
What is the energy of an electron in the n=5 state of a hydrogen atom?
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How much energy is released when an electron transitions from the n = 5 state to the n = 2 state in a hydrogen atom?
How much energy is released when an electron transitions from the n = 5 state to the n = 2 state in a hydrogen atom?
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What is the value of the atomic number Z for a hydrogen atom?
What is the value of the atomic number Z for a hydrogen atom?
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Using the wavelength-energy relationship, what is the wavelength of a photon emitted during the transition from n = 5 to n = 2?
Using the wavelength-energy relationship, what is the wavelength of a photon emitted during the transition from n = 5 to n = 2?
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What is the purpose of the slit placed in front of the cathode gun?
What is the purpose of the slit placed in front of the cathode gun?
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How do the electric and magnetic fields influence the path of the electron beam?
How do the electric and magnetic fields influence the path of the electron beam?
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What does the formula $F = eE$ represent in the context of the electron beam?
What does the formula $F = eE$ represent in the context of the electron beam?
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What change occurs to the potential energy of the electrons as they move towards the anode?
What change occurs to the potential energy of the electrons as they move towards the anode?
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What condition is necessary for the beam to have zero overall deflection?
What condition is necessary for the beam to have zero overall deflection?
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What is the significance of the mass $m$ and charge $e$ of the electron in the equations presented?
What is the significance of the mass $m$ and charge $e$ of the electron in the equations presented?
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Which material is primarily used to coat the filament in the cathode?
Which material is primarily used to coat the filament in the cathode?
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In the context of the apparatus, what role does the screen coated with zinc sulphide play?
In the context of the apparatus, what role does the screen coated with zinc sulphide play?
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What does the equation $E = \frac{me^4 Z^2}{8\pi\epsilon_o h n^2} (\frac{1}{n_1^2} - \frac{1}{n_2^2})$ represent in the context of atomic spectra?
What does the equation $E = \frac{me^4 Z^2}{8\pi\epsilon_o h n^2} (\frac{1}{n_1^2} - \frac{1}{n_2^2})$ represent in the context of atomic spectra?
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Which factor does NOT influence the frequency of radiation emitted by an atom according to the given equations?
Which factor does NOT influence the frequency of radiation emitted by an atom according to the given equations?
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In the context of Bohr's model, what value of n corresponds to the first orbit of a hydrogen atom?
In the context of Bohr's model, what value of n corresponds to the first orbit of a hydrogen atom?
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What type of spectrum consists of distinct lines representing specific frequencies emitted by an atom?
What type of spectrum consists of distinct lines representing specific frequencies emitted by an atom?
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Which equation correctly relates frequency $f$, energy difference $E$, and Planck's constant $h$?
Which equation correctly relates frequency $f$, energy difference $E$, and Planck's constant $h$?
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What does the radius of a hydrogen atom's first orbit measure to be, based on the given calculations?
What does the radius of a hydrogen atom's first orbit measure to be, based on the given calculations?
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How does an absorption spectrum differ from an emission spectrum?
How does an absorption spectrum differ from an emission spectrum?
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What constant is used in the formula for calculating the energy difference between two energy levels?
What constant is used in the formula for calculating the energy difference between two energy levels?
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What is the wavelength (in nm) of the transition from n = 2 to n = 1 in the Lyman series?
What is the wavelength (in nm) of the transition from n = 2 to n = 1 in the Lyman series?
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What energy difference (∆E) corresponds to the transition from n = 2 to n = 1?
What energy difference (∆E) corresponds to the transition from n = 2 to n = 1?
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Which of the following formulas relates the energy difference to wavelength?
Which of the following formulas relates the energy difference to wavelength?
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If electrons are accelerated through 12.0 V, which state can they excite a hydrogen atom to?
If electrons are accelerated through 12.0 V, which state can they excite a hydrogen atom to?
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What is the series limit wavelength emitted when the electron falls from n = ∞ to n = 2?
What is the series limit wavelength emitted when the electron falls from n = ∞ to n = 2?
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How is the distance of closest approach (b) in Rutherford's model related to the scattering angle (θ)?
How is the distance of closest approach (b) in Rutherford's model related to the scattering angle (θ)?
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What is the energy difference (∆E) for the transition from n = 3 to n = 1 state?
What is the energy difference (∆E) for the transition from n = 3 to n = 1 state?
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Which transition produces the longest wavelength in the Lyman series?
Which transition produces the longest wavelength in the Lyman series?
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Study Notes
Experiment Setup
- J.J. Thomson's modified apparatus consists of a discharge tube at low pressure
- The cathode emits electrons due to low-tension voltage applied across it
- A collimated beam is produced by a slit placed in front of the cathode gun
- Electrodes D and E apply an electric field perpendicular to the beam
- A magnetic field perpendicular to both the electric field and beam is also applied.
- A screen coated with zinc sulphide acts as a fluorescent material for the electron beam
- The electron beam will hit the screen at point 'M’ in the absence of any electric or magnetic field
Experiment Theory
- The electric field deflects the electron beam
- The magnetic field then forces the beam back to point 'M'
- The forces due to the electric and magnetic fields balance
- The forces on the electrons are: F=eE for electric field and F=Bev for magnetic field.
- Setting these forces equal to each other allows for finding the electron velocity
Electrons and Energy
- The electrons at the cathode possess potential energy of eV
- As the electrons proceed towards the anode, potential energy gets converted into kinetic energy.
- The frequency of emitted radiation when an electron falls from an upper to lower energy level is given by Planck's formula: E = hf
- The values of energy levels can be calculated by Bohr’s formula
Bohr's Model
- The diameter of a hydrogen atom is about 0.1 nm, consisting of a proton nucleus and a single electron
- The de Broglie wave of the electron must resonate within the orbit
- The centripetal force keeping the electron in orbit is due to the Coulomb attraction between the nucleus and the electron
- The radii of stable orbits can be calculated using Bohr's formula
- The energy of the atom in the nth state can also be calculated by Bohr's formula
- For an atom with a nucleus of charge Ze orbited by one electron, the relevant radii and energy equations are given by Bohr's formula
Atomic Spectra
- There are two main types of spectrum
- Emission spectrum: Light is emitted by a source
- Absorption spectrum: Light from a source is absorbed by a material
- Emission spectra can be broken down into two types
- Continuous spectrum: Contains all wavelengths in a specific region
- Line spectrum: Contains specific lines each with a certain frequency/wavelength/colour
- The Lyman series is the set of lines due to transitions to the ground state (n = 1)
Rutherford's Model
- The distance of closest approach (impact parameter) is related to the scattering angle by the formula: cot(𝜃/2) = 4π𝜀obT / Z𝑒2
- This distance represents how close the alpha particle gets to the nucleus
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Description
Explore the principles behind J.J. Thomson's experiment with the electron beam. This quiz covers the setup, theory, and interactions of the electric and magnetic fields affecting electron motion. Test your understanding of how these forces balance to determine the velocity of electrons.
