The circumference of second orbit of hydrogen atom, if the wavelength of electron is `5 xx 10^(-9)m` will be

Options

A. `5 xx 10^(-8)m`
B. `10^(-8)m`
C. `10^(-10)m`
D. `10^(-18)m`

Answer

To find the circumference of the second orbit of a hydrogen atom given the wavelength of the electron, we can follow these steps:

### Step 1: Understand the relationship between wavelength and circumference
The circumference of an orbit can be related to the wavelength of the electron. According to de Broglie's hypothesis, the wavelength (λ) of a particle is related to its momentum. For an electron in an orbit, the circumference (C) of the orbit is an integer multiple of the wavelength.

### Step 2: Use the formula for circumference
The formula for the circumference of an orbit is given by:
\[ C = 2 \pi r \]
where \( r \) is the radius of the orbit.

### Step 3: Relate the wavelength to the circumference
For an electron in a stable orbit, the circumference is equal to one wavelength (for the fundamental mode) or an integer multiple of the wavelength. In this case, we will consider the second orbit, where the circumference is equal to the wavelength:
\[ C = n \cdot \lambda \]
For the second orbit, \( n = 2 \):
\[ C = 2 \cdot \lambda \]

### Step 4: Substitute the given wavelength
Given that the wavelength \( \lambda = 5 \times 10^{-9} \, m \):
\[ C = 2 \cdot (5 \times 10^{-9} \, m) \]

### Step 5: Calculate the circumference
Now, calculate the circumference:
\[ C = 10 \times 10^{-9} \, m = 1 \times 10^{-8} \, m \]

### Final Answer
The circumference of the second orbit of the hydrogen atom is:
\[ C = 1 \times 10^{-8} \, m \]

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