Concept explainers
The three longest wavelengths of the photon that the singly ionized helium atoms will absorb strongly.
Answer to Problem 26SP
Solution:
Explanation of Solution
Given data:
The helium atom is singly ionized.
Formula used:
The expression for the energy of an atom having a single electron in the
Here,
The expression for the difference between the two energy levels is written as
Here,
The expression for the difference between the two energy levels is written as
Here,
Explanation:
The minimum energies of the photon will be observed for the transition of electron from
Now, the singly ionized helium atom behaves like a hydrogen atom. And, the wavelength of the photon emitted during the transition from higher to lower state will be equal to the wavelength of the photon absorbed during the transition from lower to higher state.
Now, recall the expression for energy of the atom in the
Substitute
This is the ground state energy of the singly ionized helium atom.
Similarly, substitute
This is the first excited state energy of the singly ionized helium atom.
Similarly, substitute
This is the second excited state energy of the singly ionized helium atom.
Again, substitute
This is the third excited state energy of the singly ionized helium atom.
Write the expression for the difference of energy for the transition of electron from
Substitute
Write the expression for energy of the photon emitted for the transition of electron from
Here,
Rearrange the expression for
Substitute
Write the expression for the difference of energy for the transition of electron from
Substitute
Write the expression for energy of the photon emitted for the transition of electron from
Here,
Rearrange the expression for
Substitute
Write the expression for the difference of energy for the transition of electron from
Substitute
Write the expression for energy of the photon emitted for the transition of electron from
Here,
Rearrange the expression for
Substitute
Conclusion:
Since the wavelength of the photon emitted during the transition from higher to lower state will be equal to the wavelength of the photon absorbed during the transition from lower to higher state, the three longest wavelengths of the photon, that the singly ionized helium atoms will absorb strongly, are
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Chapter 43 Solutions
Schaum's Outline of College Physics, Twelfth Edition (Schaum's Outlines)
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