Assertion (A): The potential energy of an electron revolving in any stationary orbit in a hydrogen atom is positive.
Reason (R): The total energy of a charged particle is always positive.
Assertion (A): The potential energy of an electron revolving in any stationary orbit in a hydrogen atom is positive.
Reason (R): The total energy of a charged particle is always positive.
Show Hint
- Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A)
- Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).
- Assertion (A) is true, but Reason (R) is false.
- Assertion (A) is false and Reason (R) is also false.
The Correct Option is D
Solution and Explanation
Analyzing the assertion and reason given for a hydrogen atom's electron:
Assertion (A): The potential energy of an electron revolving in any stationary orbit in a hydrogen atom is positive.
Reason (R): The total energy of a charged particle is always positive.
To evaluate these statements, consider the concept of potential and total energies in atomic physics:
- The potential energy (PE) of an electron in a hydrogen atom is negative because it is related to the attractive force between the negatively charged electron and the positively charged nucleus. The potential energy is calculated as PE = -ke²/r, where k is Coulomb's constant, e is the elementary charge, and r is the radius of the orbit. This energy is negative due to the attractive interaction.
- The total energy (E) of an electron in its orbit is also negative in a bound system like the hydrogen atom. Total energy is the sum of kinetic energy (KE) and potential energy, with E = KE + PE. In stable, bound systems, the total energy is less than zero, which means it is negative.
Conclusion: Given these insights:
- Assertion (A) is false. The potential energy of an electron in a stationary orbit in a hydrogen atom is negative, not positive.
- Reason (R) is false. The total energy of a charged particle in a bound system like a hydrogen atom is not always positive; it is usually negative.
Thus, the correct option is:
Assertion (A) is false and Reason (R) is also false.
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