Concept explainers
Consider the following energy levels of a hypothetical atom:
E4: −1.0 × 10−19 J
E3: −5.0 × 10−19 J
E2: −10 × 10−19 J
E1: −15 × 10−19 J
(a) What is the wavelength of the photon needed to excite an electron from E1 to E4? (b) What is the energy (in joules) a photon must have in order to excite an electron from E2 to E3? (c) When an electron drops from the E3 level to the E1 level, the atom is said to undergo emission. Calculate the wavelength of the photon emitted in this process.
(a)
Interpretation:
The wavelength of the photon needed to excite an electron from the given energy levels of a hypothetical atom
Concept Introduction:
The emission of radiation given by an energized hydrogen atom to the electron falling from a higher-energy orbit to a lower orbit give a quantum of energy in the form of light. Based on electrostatic interaction and law of motion, Bohr derived the following equation.
Where,
The electrons are excited thermally when the light is used by an object. As a result, an emission spectrum comes. Line spectra consist of light only at specific, discrete wavelengths. In emission, the electron returns to a lower energy state from
This transition results in the photon’s emission with frequency
When,
Answer to Problem 3.44QP
The wavelength of the photon needed to excite an electron from the given energy levels of a hypothetical atom
Explanation of Solution
To find: Calculate the wavelength of the photon needed to excite an electron from the given energy levels of a hypothetical atom
The given energy levels of a hypothetical atom are given as follows:
The energy difference (
Therefore, the energy difference (
Planck’s constant,
Therefore, the wavelength of the photon needed to excite an electron from the given energy levels of a hypothetical atom
(b)
Interpretation:
The wavelength of the photon needed to excite an electron from the given energy levels of a hypothetical atom
Concept Introduction:
The emission of radiation given by an energized hydrogen atom to the electron falling from a higher-energy orbit to a lower orbit give a quantum of energy in the form of light. Based on electrostatic interaction and law of motion, Bohr derived the following equation.
Where,
The electrons are excited thermally when the light is used by an object. As a result, an emission spectrum comes. Line spectra consist of light only at specific, discrete wavelengths. In emission, the electron returns to a lower energy state from
This transition results in the photon’s emission with frequency
When,
Answer to Problem 3.44QP
The energy of a photon to excite an electron from
Explanation of Solution
To find: Calculate the energy (in joules) a photon must have in order to excite an electron from
The energy difference (
Substitute the given values in the formula:
Therefore, the energy of a photon to excite an electron from
(c)
Interpretation:
The wavelength of the photon needed to excite an electron from the given energy levels of a hypothetical atom
Concept Introduction:
The emission of radiation given by an energized hydrogen atom to the electron falling from a higher-energy orbit to a lower orbit give a quantum of energy in the form of light. Based on electrostatic interaction and law of motion, Bohr derived the following equation.
Where,
The electrons are excited thermally when the light is used by an object. As a result, an emission spectrum comes. Line spectra consist of light only at specific, discrete wavelengths. In emission, the electron returns to a lower energy state from
This transition results in the photon’s emission with frequency
When,
Answer to Problem 3.44QP
The wavelength of the photon emitted when an electron drops from the
Explanation of Solution
To find: Calculate the wavelength of the photon emitted when an electron drops from the
The energy difference (
Therefore, the energy difference (
Planck’s constant,
Therefore, the wavelength of the photon emitted when an electron drops from the
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