The total energy of electron in an atom is a combination of potential energy and kinetic energy. If total energy is `-E` for an electron in an atom, then its K.E. and P.E. respectively are 

Options

A. 2E, -E
B. 2E, E
C. E, -2E
D. E, -E

Answer

To solve the problem, we need to understand the relationship between the total energy (E), kinetic energy (K.E.), and potential energy (P.E.) of an electron in an atom. The total energy of the electron is given by the equation:

\[ E = K.E. + P.E. \]

Given that the total energy \( E \) is \( -E \), we can express this as:

\[ -E = K.E. + P.E. \]

Let's denote the kinetic energy as \( K \) and the potential energy as \( U \). Therefore, we can rewrite the equation as:

\[ -E = K + U \]

Now, we know from quantum mechanics that for a bound electron in an atom, the potential energy is typically negative and is related to the kinetic energy. In a hydrogen-like atom, the relationship between kinetic energy and potential energy can be expressed as:

\[ K.E. = -\frac{1}{2} P.E. \]

From this relationship, we can express potential energy in terms of kinetic energy:

\[ P.E. = -2 K.E. \]

Now, substituting this into the total energy equation:

\[ -E = K + (-2K) \]
\[ -E = K - 2K \]
\[ -E = -K \]

This implies that:

\[ K.E. = E \]
\[ P.E. = -2E \]

Since we are given that the total energy \( E \) is \( -E \), we can substitute \( -E \) into our equations:

1. Kinetic Energy \( K.E. = -E \)
2. Potential Energy \( P.E. = -2(-E) = 2E \)

Thus, the kinetic energy and potential energy of the electron in the atom are:

- K.E. = \( \frac{E}{2} \)
- P.E. = \( -2E \)

### Final Answer:
- K.E. = \( \frac{E}{2} \)
- P.E. = \( -2E \)