The energy corresponding to second line of Balmer series for hydrogen atom will be:

Options

A. 2.55eV
B. 12.1eV
C. 13.6eV
D. 19.1eV

Answer

To find the energy corresponding to the second line of the Balmer series for the hydrogen atom, we can follow these steps:

### Step 1: Understand the Balmer Series
The Balmer series corresponds to transitions where the electron falls to the second energy level (n1 = 2) from higher energy levels (n2 = 3, 4, 5, ...). The second line of the Balmer series specifically refers to the transition from n2 = 4 to n1 = 2.

### Step 2: Use the Energy Level Formula
The energy levels of the hydrogen atom are given by the formula:
\[ E_n = -\frac{13.6 \, \text{eV}}{n^2} \]
where \( n \) is the principal quantum number.

### Step 3: Calculate the Energy for n1 = 2
For the lower energy level (n1 = 2):
\[ E_1 = -\frac{13.6 \, \text{eV}}{2^2} = -\frac{13.6 \, \text{eV}}{4} = -3.4 \, \text{eV} \]

### Step 4: Calculate the Energy for n2 = 4
For the higher energy level (n2 = 4):
\[ E_2 = -\frac{13.6 \, \text{eV}}{4^2} = -\frac{13.6 \, \text{eV}}{16} = -0.85 \, \text{eV} \]

### Step 5: Calculate the Energy Difference (ΔE)
Now, we find the energy difference (ΔE) between these two levels:
\[ \Delta E = E_2 - E_1 \]
Substituting the values we calculated:
\[ \Delta E = (-0.85 \, \text{eV}) - (-3.4 \, \text{eV}) \]
\[ \Delta E = -0.85 + 3.4 = 2.55 \, \text{eV} \]

### Conclusion
The energy corresponding to the second line of the Balmer series for the hydrogen atom is:
\[ \Delta E = 2.55 \, \text{eV} \]