In Bohr 's model of hydrogen when an electron jumps from n=1 to n=3 how much energy will be abosrbed

Options

A. `2.15 xx10^(-10)` ergs
B. `0.1936 xx10^(-10)` ergs
C. `2.389 xx 10^(-10)` ergs
D. `0.239 xx 10^(-10)` ergs

Answer

To solve the problem of how much energy is absorbed when an electron jumps from n=1 to n=3 in Bohr's model of hydrogen, we can follow these steps:

### Step 1: Understand the Energy Levels
In Bohr's model, the energy of an electron in the nth orbit is given by the formula:
\[ E_n = -\frac{13.6 \, \text{eV}}{n^2} \]
where \( n \) is the principal quantum number.

### Step 2: Calculate the Energy at n=1
For \( n = 1 \):
\[ E_1 = -\frac{13.6 \, \text{eV}}{1^2} = -13.6 \, \text{eV} \]

### Step 3: Calculate the Energy at n=3
For \( n = 3 \):
\[ E_3 = -\frac{13.6 \, \text{eV}}{3^2} = -\frac{13.6 \, \text{eV}}{9} = -1.511 \, \text{eV} \]

### Step 4: Calculate the Energy Absorbed
The energy absorbed when the electron jumps from n=1 to n=3 is given by the difference in energy levels:
\[ \Delta E = E_3 - E_1 \]
Substituting the values we calculated:
\[ \Delta E = (-1.511 \, \text{eV}) - (-13.6 \, \text{eV}) = -1.511 + 13.6 = 12.089 \, \text{eV} \]

### Step 5: Convert eV to ERG
To convert the energy from electron volts to ergs, we use the conversion factor:
\[ 1 \, \text{eV} = 1.602 \times 10^{-12} \, \text{erg} \]
Thus,
\[ \Delta E = 12.089 \, \text{eV} \times 1.602 \times 10^{-12} \, \text{erg/eV} = 1.937 \times 10^{-11} \, \text{erg} \]

### Final Answer
The energy absorbed when the electron jumps from n=1 to n=3 is approximately:
\[ \Delta E \approx 1.937 \times 10^{-11} \, \text{erg} \]