Energy of electron is given by `E=-2.178xx10^(-18)((Z^(2))/(n^(2)))`J.
Wavelength of light required to excited an electron in an hydrogen atom from level n=1 to n=2 will be `(h=6.62xx10^(-34)J*s and c=3.0xx10^(8)m*s^(-1))`-

Options

A. `1.214xx10^(-7)m`
B. `2.816xx10^(-7)m`
C. `6.500xx10^(-7)m`
D. `8.500xx10^(-7)m`

Explanation

To solve the problem of finding the wavelength of light required to excite an electron in a hydrogen atom from level \( n=1 \) to \( n=2 \), we will follow these steps:

### Step 1: Identify the Energy Levels
The energy of an electron in a hydrogen atom is given by the formula:
\[ E = -2.178 \times 10^{-18} \frac{Z^2}{n^2} \text{ J} \]
For hydrogen, \( Z = 1 \). Therefore, the energy levels for \( n=1 \) and \( n=2 \) are:
- For \( n=1 \):
\[ E_1 = -2.178 \times 10^{-18} \frac{1^2}{1^2} = -2.178 \times 10^{-18} \text{ J} \]
- For \( n=2 \):
\[ E_2 = -2.178 \times 10^{-18} \frac{1^2}{2^2} = -2.178 \times 10^{-18} \times \frac{1}{4} = -5.445 \times 10^{-19} \text{ J} \]

### Step 2: Calculate the Energy Difference
The energy required to excite the electron from \( n=1 \) to \( n=2 \) is given by:
\[ \Delta E = E_2 - E_1 \]
Substituting the values we calculated:
\[ \Delta E = -5.445 \times 10^{-19} - (-2.178 \times 10^{-18}) = -5.445 \times 10^{-19} + 2.178 \times 10^{-18} \]
\[ \Delta E = 1.6335 \times 10^{-18} \text{ J} \]

### Step 3: Relate Energy to Wavelength
The energy of a photon is also given by the equation:
\[ E = \frac{hc}{\lambda} \]
Where:
- \( h = 6.626 \times 10^{-34} \text{ J s} \)
- \( c = 3.0 \times 10^8 \text{ m/s} \)

Setting the two expressions for energy equal gives:
\[ \frac{hc}{\lambda} = \Delta E \]
Rearranging for \( \lambda \):
\[ \lambda = \frac{hc}{\Delta E} \]

### Step 4: Substitute the Values
Substituting the known values:
\[ \lambda = \frac{(6.626 \times 10^{-34} \text{ J s})(3.0 \times 10^8 \text{ m/s})}{1.6335 \times 10^{-18} \text{ J}} \]
Calculating the numerator:
\[ hc = 6.626 \times 10^{-34} \times 3.0 \times 10^8 = 1.9878 \times 10^{-25} \text{ J m} \]
Now substituting this into the equation for \( \lambda \):
\[ \lambda = \frac{1.9878 \times 10^{-25}}{1.6335 \times 10^{-18}} \approx 1.216 \times 10^{-7} \text{ m} \]

### Step 5: Convert to Appropriate Units
To express this in nanometers (1 nm = \( 10^{-9} \) m):
\[ \lambda \approx 121.6 \text{ nm} \]

### Final Answer
The wavelength of light required to excite an electron in a hydrogen atom from level \( n=1 \) to \( n=2 \) is approximately \( 121.6 \text{ nm} \).

---