Which of the following statements is true of hydrogen atom ?

Options

A. Angualr moment `prop(1)/(n)`
B. Linear moment `prop(1)/(n)`
C. Radius `prop (1)/(n)`
D. Energy `prop (1)/(n)`

Explanation

To determine which statement is true for the hydrogen atom, we will analyze the options provided in the question step by step.

### Step 1: Understanding Angular Momentum
The angular momentum (L) of an electron in a hydrogen atom is given by the formula:
\[ L = n \frac{h}{2\pi} \]
where \( n \) is the principal quantum number and \( h \) is Planck's constant.

### Step 2: Evaluating the First Option
The first option states that angular momentum is inversely proportional to \( n \).
From the formula, we can see that angular momentum is directly proportional to \( n \) (not inversely). Therefore, this option is incorrect.

### Step 3: Understanding Linear Momentum
Linear momentum (p) can be related to angular momentum by the equation:
\[ L = MVR \]
where \( M \) is the mass, \( V \) is the velocity, and \( R \) is the radius of the orbit.

### Step 4: Evaluating Linear Momentum
From the angular momentum equation, we can express linear momentum as:
\[ p = MV = \frac{L}{R} \]
Since we know that \( R \) (the radius of the orbit) is proportional to \( n^2 \), we can substitute this into our equation:
\[ p = \frac{n \frac{h}{2\pi}}{R} \]
This implies:
\[ p \propto \frac{n}{n^2} \]
Thus, we find that:
\[ p \propto \frac{1}{n} \]
This shows that linear momentum is inversely proportional to \( n \). Therefore, this option is correct.

### Step 5: Evaluating Energy
The energy of the electron in a hydrogen atom is given by:
\[ E \propto -\frac{1}{n^2} \]
This means that energy is inversely proportional to the square of \( n \), which does not support the statement that energy is directly proportional to \( n \). Therefore, this option is incorrect.

### Conclusion
The only true statement regarding the hydrogen atom is that linear momentum is inversely proportional to \( n \).

### Final Answer
**The correct statement is: Linear momentum is inversely proportional to \( n \).**

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