Question

The kinetic energy of an electron in the ground level in hydrogen atom is K units. The values of its potential energy and total energy respectively are_______
Fill in the blank with the correct answer from the options given below.

• A. -2K; -K
• B. +2K; -K
• C. -K; +2K
• D. +K; +2K

Answer 1

The Correct Option is A

The total energy \(E\) of an electron in an atom is given by the equation \(E = K + U\), where \(K\) is the kinetic energy and \(U\) is the potential energy. For an electron in a hydrogen atom, it is well-known that:

• The kinetic energy \(K\) is equal to \(-\frac{1}{2}E\).
• The potential energy \(U\) is twice the kinetic energy but negative, \(U = -2K\).

Given the kinetic energy of the electron is \(K\), the potential energy will be:

\[-2K\]

Similarly, the total energy \(E\) in terms of kinetic energy is:

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

Thus, the values of potential energy and total energy are:

Potential Energy: -2K

Total Energy: -K

Thus, the correct answer is: -2K; -K

Answer 2

Let's analyze the energy relationships in the hydrogen atom.

1. Kinetic Energy (KE):

The kinetic energy of an electron in the ground level of a hydrogen atom is given as K.

KE = K

2. Potential Energy (PE):

The potential energy of an electron in a hydrogen atom is related to its kinetic energy by:

PE = -2 * KE

Since KE = K:

PE = -2K

3. Total Energy (TE):

The total energy of an electron in a hydrogen atom is the sum of its kinetic and potential energies:

TE = KE + PE

TE = K + (-2K)

TE = -K

Therefore, the potential energy is -2K, and the total energy is -K.

The correct answer is:

Option 1: -2K; -K