If `[Cu(H_(2)O)_(4)]^(2+)` absorbs a light of wavelength 600 mm for d-d transition , then the value of octahedral crystal field splitting energy for `[Cu(H_(2)O)_(6)]^(2+)` will be __________ `xx 10^(-21)` J .
(Given : h = `6.63 xx 10^(-34) " Js and c "= 3.08 xx 10^(8) ms^(-1)`)

Explanation

To find the octahedral crystal field splitting energy (Δ) for the complex \([Cu(H_2O)_6]^{2+}\), we can use the relationship between energy, wavelength, and the constants provided. The energy associated with the absorbed light can be calculated using the formula:

\[ E = \frac{hc}{\lambda} \]

where:
- \(E\) is the energy in joules,
- \(h\) is Planck's constant (\(6.63 \times 10^{-34} \, \text{Js}\)),
- \(c\) is the speed of light (\(3.08 \times 10^{8} \, \text{ms}^{-1}\)),
- \(\lambda\) is the wavelength in meters.

### Step 1: Convert the wavelength from mm to meters
The given wavelength is \(600 \, \text{mm}\). We need to convert this to meters:
\[ \lambda = 600 \, \text{mm} = 600 \times 10^{-3} \, \text{m} = 0.6 \, \text{m} \]

### Step 2: Substitute the values into the energy formula
Now we can substitute the values into the energy formula:
\[ E = \frac{(6.63 \times 10^{-34} \, \text{Js}) \times (3.08 \times 10^{8} \, \text{ms}^{-1})}{0.6 \, \text{m}} \]

### Step 3: Calculate the energy
Calculating the numerator:
\[ 6.63 \times 10^{-34} \times 3.08 \times 10^{8} = 2.04284 \times 10^{-25} \, \text{Jm} \]

Now, divide by the wavelength:
\[ E = \frac{2.04284 \times 10^{-25} \, \text{Jm}}{0.6 \, \text{m}} = 3.40473 \times 10^{-25} \, \text{J} \]

### Step 4: Express the energy in the required format
To express the energy in the form of \(xx \times 10^{-21} \, \text{J}\), we convert:
\[ E = 3.40473 \times 10^{-25} \, \text{J} = 0.0340473 \times 10^{-21} \, \text{J} \approx 3.40 \times 10^{-24} \, \text{J} \]

### Final Answer
Thus, the octahedral crystal field splitting energy for \([Cu(H_2O)_6]^{2+}\) is approximately:
\[ \text{Answer: } 3.40 \times 10^{-24} \, \text{J} \]