Which of the following statements about the Bohr model of the hydrogen atom is false ?

Options

A. Acceleration of electron in `n = 2` orbit is less than that in `n = 1` orbit
B. Angular momentum of electron in `n = 2` orbit is more than that in `n = 1` orbit
C. Kinetic energy of electron in `n = 2` orbit is less than that in `n = 1` orbit
D. Potential energy of electron in `n = 2` orbit is less than that in `n = 1` orbit

Explanation

To determine which statement about the Bohr model of the hydrogen atom is false, we will analyze each statement step by step.

### Step 1: Analyze Statement A
**Statement A:** The acceleration of the electron in n = 2 orbit is less than in n = 1 orbit.

- In the Bohr model, the centripetal acceleration \( a \) of an electron in orbit is given by \( a = \frac{v^2}{r} \).
- The velocity \( v \) is proportional to \( \frac{Z}{n} \) and the radius \( r \) is proportional to \( \frac{n^2}{Z} \).
- Therefore, the acceleration can be expressed as:
\[ a \propto \frac{v^2}{r} \propto \frac{Z^2}{n^4} \]
- As \( n \) increases, \( a \) decreases. Thus, the statement is **true**.

### Step 2: Analyze Statement B
**Statement B:** The angular momentum of the electron in n = 2 orbit is more than in n = 1 orbit.

- The angular momentum \( L \) is given by \( L = n \frac{h}{2\pi} \).
- As \( n \) increases, \( L \) increases.
- Therefore, the angular momentum in n = 2 is greater than in n = 1. This statement is **true**.

### Step 3: Analyze Statement C
**Statement C:** The kinetic energy of the electron in n = 2 is less than in n = 1.

- The kinetic energy \( KE \) is given by \( KE \propto -\frac{Z}{n^2} \).
- As \( n \) increases, the kinetic energy decreases.
- Therefore, the kinetic energy in n = 2 is indeed less than in n = 1. This statement is **true**.

### Step 4: Analyze Statement D
**Statement D:** The potential energy of the electron in n = 2 orbit is greater than in n = 1 orbit.

- The potential energy \( PE \) is given by \( PE \propto -\frac{Z}{n} \).
- As \( n \) increases, the potential energy becomes less negative (or increases).
- Therefore, the potential energy in n = 2 is greater than in n = 1. This statement is **false**.

### Conclusion
The false statement among the given options is **Statement D**.

### Final Answer
**D** is the false statement regarding the Bohr model of the hydrogen atom.

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