In the Bohr model, if an electron moves in an orbit of greater radius

Options

A. Its total energy increases but its kinetic energy decreases
B. Its total energy decreases but its kinetic energy increases
C. Its total energy as well as its kinetic energy decreases
D. Its total energy as well as its kinetic energy increascs

Answer

To solve the problem regarding the behavior of an electron in a Bohr model when it moves to an orbit of greater radius, we can follow these steps:

### Step 1: Understand the Energy Relationships in the Bohr Model
In the Bohr model of the hydrogen atom, the total energy (E) of an electron in orbit is given by the formula:
\[ E = -\frac{kZ e^2}{2r} \]
where:
- \( k \) is a constant,
- \( Z \) is the atomic number (for hydrogen, \( Z = 1 \)),
- \( e \) is the charge of the electron,
- \( r \) is the radius of the orbit.

### Step 2: Analyze the Effect of Increasing Radius
As the radius \( r \) increases, we can analyze how the total energy changes:
- The total energy \( E \) becomes less negative (i.e., it increases) because the denominator \( r \) is increasing. This means that the absolute value of the total energy is decreasing.

### Step 3: Kinetic Energy in the Bohr Model
The kinetic energy (K.E.) of the electron in the orbit is given by:
\[ K.E. = \frac{kZ e^2}{2r} \]
As \( r \) increases, the kinetic energy also decreases because the denominator \( r \) is increasing.

### Step 4: Conclusion
From the analysis:
- The total energy increases (becomes less negative).
- The kinetic energy decreases.

Thus, the correct answer is that the total energy increases while the kinetic energy decreases.

### Final Answer
The total energy increases, and the kinetic energy decreases when an electron moves to an orbit of greater radius in the Bohr model.

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