The energy of `n^(th)` orbit is given by
`E_(n) = ( -Rhc)/(n^(2))`
When electron jumpsfrom one orbit to another orbit then wavelength associated with the radiation is given by
`(1)/(lambda) = RZ^(2)((1)/(n_(1)^(2)) - (1)/ (n_(2)^(2)))`
The series that belongs to visible region is

Options

A. Lyman Series
B. Balmer Series
C. Pfund Series
D. Humphrey Series

Answer

To determine which series belongs to the visible region, we can follow these steps:

### Step 1: Understand the Energy Equation
The energy of the nth orbit is given by:
\[ E_n = \frac{-Rhc}{n^2} \]
where \( R \) is the Rydberg constant, \( h \) is Planck's constant, and \( c \) is the speed of light.

### Step 2: Wavelength Calculation
When an electron jumps from one orbit to another, the wavelength associated with the radiation emitted or absorbed is given by:
\[ \frac{1}{\lambda} = RZ^2 \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right) \]
where \( Z \) is the atomic number, \( n_1 \) is the lower energy level, and \( n_2 \) is the higher energy level.

### Step 3: Identify the Visible Region
The visible region of the electromagnetic spectrum ranges from approximately 380 nm to 700 nm.

### Step 4: Identify the Series
- **Lyman series**: Transitions to \( n=1 \) (UV region)
- **Balmer series**: Transitions to \( n=2 \) (Visible region)
- **Paschen series**: Transitions to \( n=3 \) (IR region)
- **Humphreys series**: Transitions to \( n=4 \) and higher (far IR region)

### Step 5: Determine the Balmer Series
The Balmer series corresponds to transitions where \( n_1 = 2 \) and \( n_2 \) can be 3, 4, 5, etc.

### Step 6: Calculate Wavelengths for Balmer Series
1. For \( n_2 = 3 \) and \( n_1 = 2 \):
\[ \frac{1}{\lambda} = RZ^2 \left( \frac{1}{2^2} - \frac{1}{3^2} \right) \]
Calculate \( \lambda \) to find the wavelength.

2. For \( n_2 = 4 \) and \( n_1 = 2 \):
\[ \frac{1}{\lambda} = RZ^2 \left( \frac{1}{2^2} - \frac{1}{4^2} \right) \]
Again, calculate \( \lambda \).

### Step 7: Compare Wavelengths
After calculating the wavelengths for the transitions in the Balmer series, check if they fall within the visible range (380 nm to 700 nm).

### Conclusion
The series that belongs to the visible region is the **Balmer series**.

---