Concept explainers
(a)
The energy required to ionize a hydrogen atom in its lowest energy level.
(a)
Answer to Problem 3SP
The energy required to ionize a hydrogen atom in its lowest energy level is
Explanation of Solution
The energy level diagram of hydrogen proposed by the
Ionization energy is the energy required to remove an electron from its orbit. It will be equal to the negative of the energy of the electron in the orbit. The energy of the electron in the lowest level of hydrogen atom is
Conclusion:
Thus the energy required to ionize a hydrogen atom in its lowest energy level is
(b)
The energy required to ionize the hydrogen atom when it is in the first excited state above the lowest level.
(b)
Answer to Problem 3SP
The energy required to ionize the hydrogen atom when it is in the first excited state above the lowest level is
Explanation of Solution
The energy level diagram of hydrogen proposed by the Bohr model gives the energy of electrons in different orbits in hydrogen atom. The energy of a particular level in the hydrogen atom is given by the ratio of
The first excited state is the level which lies just above the ground level. The energy of the first excited state of hydrogen atom is
Ionization energy is the energy required to remove an electron from its orbit. It will be equal to the negative of the energy of the electron in the orbit. This implies the energy required to ionize the hydrogen atom in the first excited state will be equal to
Conclusion:
Thus the energy required to ionize the hydrogen atom when it is in the first excited state above the lowest level is
(c)
The wavelength of the photon emitted when an ionized hydrogen atom goes to the lowest energy level after capturing an electron with zero kinetic energy.
(c)
Answer to Problem 3SP
The wavelength of the photon emitted when an ionized hydrogen atom goes to the lowest energy level after capturing an electron with zero kinetic energy is
Explanation of Solution
An ionized hydrogen atom will have zero energy. The energy of the lowest level in the hydrogen atom is
Write the equation for the energy of the photon.
Here,
Substitute
Write the equation for the energy of a photon.
Here,
Rewrite the above equation for
The value of
Substitute
Conclusion:
Thus the wavelength of the photon emitted when an ionized hydrogen atom goes to the lowest energy level after capturing an electron with zero kinetic energy is
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Chapter 18 Solutions
Physics of Everyday Phenomena
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