DSSSB TGT/PGT/PRT Exam > DSSSB TGT/PGT/PRT Questions > The ratio of kinetic energy to the total ener...
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The ratio of kinetic energy to the total energy of an electron in a Bohr orbit of the hydrogen atom is
- a)1 : 1
- b)1 : -1
- c)2 : -1
- d)1 : -2
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
The ratio of kinetic energy to the total energy of an electron in a Bo...
Understanding Kinetic Energy and Total Energy in Bohr's Model
In the context of the hydrogen atom, Bohr's model provides insightful details about the energy states of electrons. Here's a breakdown of the kinetic energy (KE) and total energy (TE) ratio.
Kinetic Energy of the Electron
- The kinetic energy (KE) of an electron in a Bohr orbit is given by the formula: KE = (1/2)mv².
- In Bohr's model, the electron moves in a circular orbit under the influence of the electrostatic force of attraction between the positively charged nucleus (proton) and the negatively charged electron.
Total Energy of the Electron
- The total energy (TE) of the electron is the sum of its kinetic energy and potential energy (PE).
- The potential energy in a hydrogen atom is negative: PE = -k(e²/r), where k is a constant, e is the charge of the electron, and r is the radius of the orbit.
- Therefore, total energy can be expressed as TE = KE + PE.
Ratio of Kinetic Energy to Total Energy
- In Bohr's model, it is derived that the kinetic energy is equal to half of the magnitude of the potential energy.
- Hence, KE = - (1/2) PE.
- The total energy can be expressed as TE = KE + PE = KE - 2KE = -KE.
This leads to the ratio:
- KE : TE = KE : (-KE) = 1 : -1.
Conclusion
The correct answer to the ratio of kinetic energy to total energy of an electron in a Bohr orbit of the hydrogen atom is indeed 1 : -1 (option b). This highlights the fundamental relationship between kinetic and potential energies in atomic structures, emphasizing stability in quantum systems.
In the context of the hydrogen atom, Bohr's model provides insightful details about the energy states of electrons. Here's a breakdown of the kinetic energy (KE) and total energy (TE) ratio.
Kinetic Energy of the Electron
- The kinetic energy (KE) of an electron in a Bohr orbit is given by the formula: KE = (1/2)mv².
- In Bohr's model, the electron moves in a circular orbit under the influence of the electrostatic force of attraction between the positively charged nucleus (proton) and the negatively charged electron.
Total Energy of the Electron
- The total energy (TE) of the electron is the sum of its kinetic energy and potential energy (PE).
- The potential energy in a hydrogen atom is negative: PE = -k(e²/r), where k is a constant, e is the charge of the electron, and r is the radius of the orbit.
- Therefore, total energy can be expressed as TE = KE + PE.
Ratio of Kinetic Energy to Total Energy
- In Bohr's model, it is derived that the kinetic energy is equal to half of the magnitude of the potential energy.
- Hence, KE = - (1/2) PE.
- The total energy can be expressed as TE = KE + PE = KE - 2KE = -KE.
This leads to the ratio:
- KE : TE = KE : (-KE) = 1 : -1.
Conclusion
The correct answer to the ratio of kinetic energy to total energy of an electron in a Bohr orbit of the hydrogen atom is indeed 1 : -1 (option b). This highlights the fundamental relationship between kinetic and potential energies in atomic structures, emphasizing stability in quantum systems.
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Community Answer
The ratio of kinetic energy to the total energy of an electron in a Bo...
According to the given formula of total energy and kinetic energy of electrons in nth orbit:
Total Energy in nth orbit (En) =
Kinetic Energy in nth orbit (K En)=
Total energy (E) = - Kinetic energy (KE)
Ratio = (KE/E) = -1/1 = 1 : -1
Total Energy in nth orbit (En) =
Kinetic Energy in nth orbit (K En)=
Total energy (E) = - Kinetic energy (KE)
Ratio = (KE/E) = -1/1 = 1 : -1
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The ratio of kinetic energy to the total energy of an electron in a Bohr orbit of the hydrogen atom isa)1 : 1b)1 : -1c)2 : -1d)1 : -2Correct answer is option 'B'. Can you explain this answer? for DSSSB TGT/PGT/PRT 2025 is part of DSSSB TGT/PGT/PRT preparation. The Question and answers have been prepared according to the DSSSB TGT/PGT/PRT exam syllabus. Information about The ratio of kinetic energy to the total energy of an electron in a Bohr orbit of the hydrogen atom isa)1 : 1b)1 : -1c)2 : -1d)1 : -2Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for DSSSB TGT/PGT/PRT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The ratio of kinetic energy to the total energy of an electron in a Bohr orbit of the hydrogen atom isa)1 : 1b)1 : -1c)2 : -1d)1 : -2Correct answer is option 'B'. Can you explain this answer?.
The ratio of kinetic energy to the total energy of an electron in a Bohr orbit of the hydrogen atom isa)1 : 1b)1 : -1c)2 : -1d)1 : -2Correct answer is option 'B'. Can you explain this answer? for DSSSB TGT/PGT/PRT 2025 is part of DSSSB TGT/PGT/PRT preparation. The Question and answers have been prepared according to the DSSSB TGT/PGT/PRT exam syllabus. Information about The ratio of kinetic energy to the total energy of an electron in a Bohr orbit of the hydrogen atom isa)1 : 1b)1 : -1c)2 : -1d)1 : -2Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for DSSSB TGT/PGT/PRT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The ratio of kinetic energy to the total energy of an electron in a Bohr orbit of the hydrogen atom isa)1 : 1b)1 : -1c)2 : -1d)1 : -2Correct answer is option 'B'. Can you explain this answer?.
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