Question

The kinetic energy of an electron in the ground level in hydrogen atom is \(K\) units. The values of potential energy and total energy, respectively, are

• A. \(-2K,\ -K\)
• B. \(+2K,\ -K\)
• C. \(-K,\ +2K\)
• D. \(+K,\ +2K\)

Hint:

For an electron in Bohr's atom: \[ U=-2K \] \[ E=K+U=-K \] Therefore, \[ K : U : E = 1 : -2 : -1 \] This relation is frequently used in atomic physics MCQs.

Answer 1

The Correct Option is A

Concept: For an electron in a hydrogen atom, \[ U=-2K \] where \[ U=\text{Potential Energy} \] and \[ K=\text{Kinetic Energy} \] The total energy is \[ E=K+U \]

Step 1:Find the potential energy. Using \[ U=-2K \] we get \[ {U=-2K} \]

Step 2: Find the total energy. \[ E=K+U \] \[ E=K+(-2K) \] \[ E=-K \] Thus, \[ {E=-K} \]

Step 3: State the answer. \[ { \begin{array}{c} \text{Potential Energy}=-2K \text{Total Energy}=-K \end{array} } \] Hence, the correct option is \[ {(A)} \]