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If the electron of a hydrogen atom is present in the first orbit, the total energy of the electron is
- a)-e2/r
- b)-e2/r2
- c)-e2/2r
- d)-e2/2r2
Correct answer is option 'D'. Can you explain this answer?
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Explanation:
The total energy of the electron in the hydrogen atom is given by the sum of its kinetic energy and potential energy.
Kinetic Energy: The electron in the first orbit of the hydrogen atom moves in a circular path with a speed of v. Its kinetic energy is given by:
KE = (1/2)mv^2
But, we know that the centripetal force acting on the electron is provided by the electrostatic force of attraction between the electron and the nucleus. Therefore, we can write:
mv^2/r = ke^2/r^2
where k is the Coulomb's constant and e is the charge of the electron.
Potential Energy: The potential energy of the electron in the hydrogen atom is given by:
PE = -ke^2/r
where the negative sign indicates that the electron is bound to the nucleus and has less energy than an electron at infinity.
Total Energy: The total energy of the electron is the sum of its kinetic and potential energies:
E = KE + PE
= (1/2)mv^2 - ke^2/r
= -ke^2/2r
Therefore, the correct option is D) -e2/2r2.
The total energy of the electron in the hydrogen atom is given by the sum of its kinetic energy and potential energy.
Kinetic Energy: The electron in the first orbit of the hydrogen atom moves in a circular path with a speed of v. Its kinetic energy is given by:
KE = (1/2)mv^2
But, we know that the centripetal force acting on the electron is provided by the electrostatic force of attraction between the electron and the nucleus. Therefore, we can write:
mv^2/r = ke^2/r^2
where k is the Coulomb's constant and e is the charge of the electron.
Potential Energy: The potential energy of the electron in the hydrogen atom is given by:
PE = -ke^2/r
where the negative sign indicates that the electron is bound to the nucleus and has less energy than an electron at infinity.
Total Energy: The total energy of the electron is the sum of its kinetic and potential energies:
E = KE + PE
= (1/2)mv^2 - ke^2/r
= -ke^2/2r
Therefore, the correct option is D) -e2/2r2.
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