According to the Bohr model of the hydrogen atom, the total energy of an electron in the nth stationary orbit is directly proportional to: MCQ with Answer and Explanation
According to the Bohr model of the hydrogen atom, the total energy of an electron in the nth stationary orbit is directly proportional to:
A. 1 / n^2
B. 1 / n
C. n^2
D. n
Answer: Option A
Solution (By JKSSB Mock Tests)
The total energy of an electron in a hydrogen-like atom in the nth orbit is strictly negative and given by the mathematical formula E_n = -13.6 Z^2 / n^2 (in eV). This formula demonstrates that the total energy is inversely proportional to the square of the principal quantum number (n^2).
Explanation:
KE = p²/(2m) = (10)²/(2×2) = 100/4 = 25 J. Wait, recalculate: 100/4 = 25 J. Option B is correct. KE = p²/2m relates momentum and kinetic energy. Memory tip: When given momentum, use KE = p²/2m instead of finding velocity first. Efficient calculation method for competitive exam time constraints.
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