Energy of the third orbit of Bohr's atom is

Options

A. `-13.6eV`
B. `-3.6eV`
C. `-1.5eV`
D. None of these

Answer

To find the energy of the third orbit of Bohr's atom, we can use the formula derived from Bohr's model of the hydrogen atom. Here’s a step-by-step solution:

### Step 1: Understand the Formula
The energy of an electron in the nth orbit of a hydrogen atom is given by the formula:
\[ E = -\frac{13.6 \, Z^2}{n^2} \]
where:
- \( E \) is the energy in electron volts (eV),
- \( Z \) is the atomic number of the element,
- \( n \) is the principal quantum number (the orbit number).

### Step 2: Identify the Values
For the third orbit:
- \( n = 3 \)
- For hydrogen, the atomic number \( Z = 1 \).

### Step 3: Substitute the Values into the Formula
Now, substitute \( Z = 1 \) and \( n = 3 \) into the formula:
\[ E = -\frac{13.6 \times (1)^2}{(3)^2} \]

### Step 4: Calculate the Energy
Now, calculate the energy:
\[ E = -\frac{13.6 \times 1}{9} \]
\[ E = -\frac{13.6}{9} \]
\[ E \approx -1.51 \, \text{eV} \]

### Step 5: Conclusion
Thus, the energy of the third orbit of Bohr's atom (hydrogen) is approximately:
\[ E \approx -1.5 \, \text{eV} \]

### Final Answer
The correct option is Option 3: -1.5 eV.

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