NEET
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- NEET
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- Atomic Physics
NEET · Physics · Atomic Physics
Given below are two statements: one is labelled as Assertion (A)...
Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): For an electron in a hydrogen atom, the total energy is always negative, which indicates that the electron is bound to the nucleus.
Reason (R): The electrostatic potential energy is negative and its magnitude is twice that of the kinetic energy.
In the light of the above statements, choose the most appropriate answer from the options given below:
Assertion (A): For an electron in a hydrogen atom, the total energy is always negative, which indicates that the electron is bound to the nucleus.
Reason (R): The electrostatic potential energy is negative and its magnitude is twice that of the kinetic energy.
In the light of the above statements, choose the most appropriate answer from the options given below:
Options
- ABoth (A) and (R) are correct and (R) is the correct explanation of (A)
- BBoth (A) and (R) are correct but (R) is not the correct explanation of (A)
- C(A) is correct but (R) is not correct
- D(A) is not correct but (R) is correct
Correct answer
A. Both (A) and (R) are correct and (R) is the correct explanation of (A)
Step-by-step solution
The total energy (TE) of an electron is the sum of its kinetic energy (KE) and potential energy (PE).
According to Reason (R), the potential energy is negative and its magnitude is twice the kinetic energy. Mathematically, .
Substituting this into the total energy equation gives:
.
Since kinetic energy is always positive, the total energy must be negative. A negative total energy physically signifies that the electron is bound to the nucleus and requires external energy to be freed.
Thus, the Reason correctly explains why the total energy is negative as stated in the Assertion. Both statements are correct, and (R) is the correct explanation of (A).
Answer: Both (A) and (R) are correct and (R) is the correct explanation of (A)
According to Reason (R), the potential energy is negative and its magnitude is twice the kinetic energy. Mathematically, .
Substituting this into the total energy equation gives:
.
Since kinetic energy is always positive, the total energy must be negative. A negative total energy physically signifies that the electron is bound to the nucleus and requires external energy to be freed.
Thus, the Reason correctly explains why the total energy is negative as stated in the Assertion. Both statements are correct, and (R) is the correct explanation of (A).
Answer: Both (A) and (R) are correct and (R) is the correct explanation of (A)