the number of de broglie wavelength contained in the second bohr orbit of hydrogen atom is

Options

A. 1
B. 2
C. 3
D. 4

Explanation

To find the number of de Broglie wavelengths contained in the second Bohr orbit of a hydrogen atom, we can follow these steps:

### Step 1: Understand the de Broglie wavelength
The de Broglie wavelength (λ) is given by the formula:
\[ \lambda = \frac{h}{mv} \]
where \( h \) is Planck's constant, \( m \) is the mass of the electron, and \( v \) is its velocity.

### Step 2: Apply Bohr's postulate
According to Bohr's model, the angular momentum of an electron in a circular orbit is quantized and is given by:
\[ mvr = n \frac{h}{2\pi} \]
where \( n \) is the principal quantum number (n = 1, 2, 3, ...).

### Step 3: Relate the circumference of the orbit to the de Broglie wavelength
The circumference of the orbit is given by:
\[ 2\pi r \]
From Bohr's postulate, we can express the circumference in terms of the de Broglie wavelength:
\[ 2\pi r = n \lambda \]

### Step 4: Substitute for the second Bohr orbit
For the second Bohr orbit, we have \( n = 2 \). Therefore, we can write:
\[ 2\pi r = 2\lambda \]
This indicates that the circumference of the second Bohr orbit contains 2 de Broglie wavelengths.

### Step 5: Conclusion
Thus, the number of de Broglie wavelengths contained in the second Bohr orbit of a hydrogen atom is:
\[ \text{Number of de Broglie wavelengths} = 2 \]

### Final Answer
The number of de Broglie wavelengths contained in the second Bohr orbit of the hydrogen atom is **2**.

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