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H-like system

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Wize University Chemistry Textbook > Early Atomic Theory to Quantum Theory

How Atomic Spectra Relates to Electronic Transitions + Other Applications of the Bohr Model

5 Activities

Wize University Chemistry Textbook > Early Atomic Theory to Quantum Theory

Wave-Particle Duality & the de Broglie Equation

4 Activities

Which of the following electron transitions for the hydrogen atom is associated with the longest photon wavelength?
More How Atomic Spectra Relates to Electronic Transitions + Other Applications of the Bohr Model Questions:
Bohr model: Absorption/Emission Spectra
An Emission spectrum for a one-electron species is shown below. The spectrum shows all lines resulting from transitions to the second excited state. The line B is 165nm.
Identify the species in the spectrum above
Bohr model
Which of the following transitions would emit the shortest wavelength photon?
Bohr Model: Emission/Absorption Spectra
Consider the generic atomic emission line spectrum and the energy diagram shown below for a species (atom or ion) with one electron.
Which emission line has the highest energy?
Bohr Model: Frequency of light
Calculate the frequency of light, in Hz, required to promote gaseous He+ ions from the first excited state to the second excited state.
A sample of Hydrogen atoms is excites such that there exists a mixture of excited states form n = 1 to n = 6. the sample is then allowed to relax back to the ground state and the emission spectrum is recorded. What is the wavelength of the highest energy photon emitted?
h = 6.626 × 10-34 J s ( J = kg m2 s-2)
c = 2.9979 × 108 m s-1
H-line spectra
An electronic transition of the one electron version of B, to the 2nd excited state, generates a line with wavelength 43.7 nm. Identify the transition.
Electromagnetic Radiation: Absorption Spectrum
You shine light through a sample of gaseous atomized hydrogen and take an absorption spectrum as shown below. Only transitions to or from the ground state (n=1) appear in the spectrum. Which of these energy-level transitions correspond to the line labelled X in the absorption spectrum?
Ionization Energy: Hydrogen
What is the ionization energy for H if its electron is in ground state?
The easiest way to solve this problem is by using the Rydberg expression:
1lambda=R(1n12−1n22)\frac{1}{lambda}=R\left(\frac{1}{n_1^2}-\frac{1}{n_2^2}\right)
Bohr model: Transition Wavelength
What is the wavelength of photon that must be absorbed by a hydrogen atom to
promote its electron from the n=3n = 3 to the n=7n = 7 level?
Bohr Model
For a collection of hydrogen atoms, if one excites their electrons to energy state n = 3, when these electrons relax back to ground state, how many photons of different energy can be emitted?
Bohr Model: Frequency of light
Calculate the frequency of light, in Hz, required to promote gaseous He+ ions from the first excited state to the second excited state.
Bohr model: Absorption/Emission Spectra
An Emission spectrum for a one-electron species is shown below. The spectrum shows all lines resulting from transitions to the second excited state. The line B is 165nm.
Identify the species in the spectrum above
Bohr Model: Frequency of emission and photoelectric effect
Calculate the frequency of light, in Hz, emitted when gaseous Be3+ ions move form n = 4 to the n = 1 state?
Calculate the frequency (Hz) and wavelength (nm) of the emitted photon when an electron drops from the n = 6 to the n = 3 level in a hydrogen atom.
Practice: H-line Spectrum
A light generated due to an electronic transition between n=3 to n=1 of Li2+ is shone on a Mg metal surface. What is the maximum kinetic energy of the emitted electrons in Joules? wMg = 3.66 eV; 1 eV = 1.60218 ⋅\cdot 10−19 J
Electromagnetic Radiation
An excited hydrogen atom emits light with a wavelength of 433.9 nm to reach the energy level for which n = 2. In which principal quantum number did the electron begin?
CHEM 1011 (Dalhousie) - Electromagnetic Radiation
An electron in a hydrogen atom is promoted from the n = 1 state to a higher energy state when it absorbs radiation with a wavelength of 97.2 nm.
a) Calculate the frequency of the absorbed radiation.
b) Calculate the energy of the absorbed radiation.
Electromagnetic Radiation
7. An excited hydrogen atom emits light with a wavelength of 397.2 nm to reach the energy level for which n = 2. In which principal quantum number did the electron begin?
Electromagnetic Radiation
5. Which of the following statements are true?
Electromagnetic Radiation and Atoms
A student observes a hydrogen Atom emits a photon of light with energy of -4.09 x 10-19 J. The student notes that the emission falls within the visible light region of the electromagnetic spectrum, meaning the final state of the electron is in the Balmer series and thus nf = 2. Based on the students observations...
a) Calculate the wavelength, in nm, of the photon emitted by the hydrogen atom. Round your answer to the nearest whole number.
b) What is the initial state, ni, of the electron before relaxation?
Below is the energy level diagram for the possible energy levels of a hydrogen atom (not to scale).
Answer following question about the hydrogen atom.
What is the wavelength of light emitted by the transition labelled D from the shown figure?
Bohr Model
Given the atomic spectrum of hydrogen below, which of the following statements is correct?
Bohr Model: Emission/Absorption Spectra
Consider the generic atomic emission line spectrum and the energy diagram shown below for a species (atom or ion) with one electron.
Which emission line has the highest energy?
Bohr Model: Frequency of light
Calculate the frequency of light, in Hz, emitted when gaseous Be3+ ions move form n = 4 to the n = 1 state? Just enter the numerical value as your answer with 3 digits (don't write units). Units are Hz.
An emission spectrum for a one-electron species is shown below. All the lines correspond to transitions ending at the energy level n = 3. Line B has a wavelength of 165 nm. Identify the species that produced this spectrum.
Identify the species in the spectrum above
Bohr Model
A photon of light was released by a helium cation (He+) with an energy of 1.8312 x 10-18 J. If this transition ended at n = 2, from which level did this transition begin?
Bohr Model: Atomic Spectra
Using Bohr’s model of hydrogen atom, can you show that no electron transitions states relaxing to a final state of n ≥3 is capable of emitting photons with a wavelength in the visible spectrum?
Calculate the wavelength of light emitted when an electron in a hydrogen atom moves from n= 1 to n = 2
The energy level diagram for an electron in a hydrogen atom (not to scale) is shown below. Answer following question with reference to this diagram.
Which transition represents the ionization of the hydrogen atom?
The Bohr Model
A photon of light was released by a hydrogen atom with an energy of 1.94 x 10-18 J. If this transition ended at n = 1, from which level did this transition begin?
How much energy would be required to completely remove an electron from the n=3 shell of a hydrogen atom?
A sample of hydrogen atoms are excited to an unknown energy level. The excited electrons relax to the ground state (n = 1) and emit a photon with a wavelength of 103nm. What energy level were the electrons in the hydrogen atom originally excited to?
Bohr model: Wavelength
A sample of Hydrogen atoms is excites such that there exists a mixture of excited states form n = 1 to n = 6. the sample is then allowed to relax back to the ground state and the emission spectrum is recorded. What is the wavelength of the highest energy photon emitted?
A sample of Hydrogen atoms is excites such that there exists a mixture of excited states form n = 1 to n = 6. the sample is then allowed to relax back to the ground state and the emission spectrum is recorded. What is the wavelength of the highest energy photon emitted?
h = 6.626 × 10-34 J s ( J = kg m2 s-2)
c = 2.9979 × 108 m s-1
An emission spectra is recorded from a sample of hydrogen. The discreet lines in the spectra come from:
Bohr model
Which of the following transitions would emit the shortest wavelength photon?
Bohr Model: Energy
Which hydrogen emission line should you expect to have the greatest energy?
Bohr model: Energy
A sample of Hydrogen atoms is excites such that there exists a mixture of excited states from n = 1 to n = 6. the sample is then allowed to relax back to the ground state and the emission spectrum is recorded. What transition produces the lowest energy photon?
Bohr model: Finding the Initial Energy Level
In the atomic emission spectra for hydrogen a line is observed at 97.25nm. What was the initial energy level for the electron before the transition occurred? The transition ends at the ground state.
Bohr model: Qualitative Emissions
Which of the following transitions would emit the shortest wavelength photon?
Periodic Trends: Ionization of an Excited Hydrogen Atom
A sample of hydrogen atoms is thermally excited so that the electrons are resting in the n=3 state. What is the wavelength of the lowest energy photon capable of ionizing these excited hydrogen atoms?
Bohr Model: Predicting Hydrogen Emission Wavelengths
Calculate the wavelength of light emitted when an electron in a hydrogen atom moves from n= 2 to n = 1.
Shown below is an energy level diagram for a hydrogen atom. Calculate the frequency of the photon associated with transition E
Shown below is an energy level diagram for a hydrogen atom. Calculate the Energy of the photon associated with transition B
Shown below is an energy level diagram for a hydrogen atom. Please choose the INCORRECT statement
Shown below is an energy level diagram for a hydrogen atom. Please choose the CORRECT statement
What is the energy change when an electron moves from the n = 7 to n = 2 energy level in a hydrogen atom?
A sample of Hydrogen atoms is excited to n = 6 and the sample is then allowed to relax back to the ground state (n = 1) and an emission spectrum is recorded. What is the wavelength photon emitted?
Bohr Model: Absorption Spectrum
You shine light through a sample of gaseous atomized hydrogen and take an absorption spectrum as shown below. Only transitions to or from the ground state (n=1) appear in the spectrum. Which of these energy-level transitions correspond to the line labelled X in the absorption spectrum?
Atom: Calculating Ionization Energy of a Hydrogen-like Ion
Calculate the ionization energy of He+. Express your answer in Joules (J).
More Wave-Particle Duality & the de Broglie Equation Questions:
Light Energy
The energy content of a particular form of light is 1.572 J per mole of photons. What is the wavelength of this light? (Choose the closest answer.)
Electromagnetic radiation: Wave energy
A laser emits light at a wavelength of 710 nm.
What is the frequency of this light?
What is the de Broglie wavelength of a 20 kg dog? (Note: 1 J  = 1 kg m2s21\ J\ \ =\ 1\ kg\ \frac{m^2}{s^2})
If a photon was able to remove an electron from a metal plate that had a binding energy of 2 x 10-20 J, what was the frequency of the wave?
If the answer has an exponent write it like this 1.23x10^4 (no spaces)
Light and EM Multipart Question
You have a laser that emits light at a wavelength of 710 nm.
Electromagnetic radiation: Wave energy
A laser emits light at a wavelength of 710 nm.
What is the frequency of this light?
Work Function
The work function of metallic cesium is 3.36×10−19 J. What is the threshold wavelength of light required to emit electrons from the surface of metallic cesium?
Light Energy
The energy content of a particular form of light is 1.572 J per mole of photons. What is the wavelength of this light? (Choose the closest answer.)
H atom
A hydrogen atom, initially in its lowest energy level, absorbs a photon with a wavelength of 93.1 nm. What is the final energy level?
de Broglie wavelength
Which of the following objects has the longest de Broglie wavelength? Assume they are all moving at the same speed.
Wave particle duality
The wavelike character of ordinary objects like a thrown baseball cannot be detected because:
Energy of Light
A domestic microwave generates radiation of wave length 9.3 cm (very low energy).
a. What are the energy values per photon and per mole of of photons?
b. Calculate the frequency of this radiation
Water can absorb infrared radiation at a wavelength of1.06×104 m{\small 1.06\times10^4 \text{ m}}. If a 180 g sample of water is irradiated at this wavelength, calculate the number of photons required to raise the temperature by 25.0°C(CH2O=4.184Jg°C){\small \degree \text{C} \left(C_{H_2O} =4.184\frac{J}{g\degree C} \right)}
Electromagnetic radiation: Wave Energy
Calculate the energy of one photon whose wavelength is 589 nm.
How heavy is a particle whose de Broglie wavelength is 1.87 x 10-16 m?
Practice Problem 1: de Broglie Equation
What is the energy associated with the de Broglie wavelength of a 1000 kg car? ((1 J = 1kgm2s2)\left(1\ J\ =\ 1kg\frac{m^2}{s^2}\right)
An emission spectrum for a one-electron species is shown below. All the lines correspond to transitions ending at the energy level n = 3. Line B has a wavelength of 165 nm. Identify the species that produced this spectrum.
Identify the species in the spectrum above
If a photon was able to remove an electron from a metal plate that had a binding energy of 2 x 10-20 J, what was the frequency of the wave?
Wave Particle Duality: de Broglie's Postulate
Calculate the de Broglie wavelength for the following objects. For each one decide whether they are best treated as classical or quantum mechanical particles
A proton moving at 1% of the speed of light
How heavy is a particle whose de Broglie wavelength is 1.87 x 10-16 m?
What is the de Broglie wavelength of a 20 kg dog? (Note: 1 J  = 1 kg m2s21\ J\ \ =\ 1\ kg\ \frac{m^2}{s^2})
Wave Particle Duality and the Heisenberg Uncertainty Principle
A beam of electrons is accelerated towards a thin metal foil and diffracts to give the exact same pattern as a blue laser with wavelength of 480nm. (me = 9.11 x 10-31 kg)
a) What speed were the electrons accelerated to?'
b) If we measure the speed to a precision of ± 1% what is the minimum uncertainty in the position of the electron?
A proton (mp = 1.6726 x 10-27 kg) was found to have a de Broglie wavelength of 522 nm. How fast was the particle moving?
Quantum Model: de Broglie's Equation
What is the energy associated with the de Broglie wavelength of a 1000 kg car? ((1 J = 1 kgm2s2)\left(1\ J\ =\ 1\ kg\frac{m^2}{s^2}\right)
Wave-Particle Duality: Wave Energy
Scientists in the lab were preparing a new chemical reaction. Upon mixing the chemicals, the reaction began to emit a great deal of light. The scientists were able to determine that each photon of light was releasing 8.32 x 10-19 J of energy. What is the wavelength of this light? What is the frequency?
Wave Particle Duality: de Broglie's Postulate
The electrons used in electron microscopy have a velocity of 70% of the speed of light. What is their wavelength in nm?
The reason that we can't measure the position and velocity of a particle to infinite precision is?
What wavelength of light corresponds to a transition from a 6p orbital to a 1s orbital in hydrogen?
Report your answer to three significant figures in nm. Please do not include units in the answer field.
The experiment that showed electrons can behave like waves is the:
de Broglie's postulate: Wavelength of Lance Armstrong
During the tour de France in 2010, Lance Armstrong reached a speed of 57.8km/h descending one of the mountains. If we treat Lance and his bike as a single particle with a weight of 100kg what is the wavelength of Lance Armstrong?
Young's Double-Slit Experiment
If you shoot a beam of electrons at a piece of metal with two small slits in it, a diffraction pattern appears on the detector on the otherside. This is often refereed to as a two slit experiment. This result shows that,
What is the wavelength of an electron traveling at 5% the speed of light?