The value of Planck's constant is `6.63 xx 10^-34 Js`. The speed of light is `3 xx 10^(17)nms^(-1)`. Which value is closest to the wavelength of quantum of light with frequency of `6 xx 10^15 sec^-1` ?

Options

A. 25
B. 50
C. 75
D. 10

Explanation

To find the wavelength of the quantum of light with a given frequency, we can use the formula that relates the speed of light (c), wavelength (λ), and frequency (ν):

\[ c = \lambda \cdot \nu \]

Where:
- \( c \) is the speed of light,
- \( \lambda \) is the wavelength,
- \( \nu \) is the frequency.

### Step 1: Rearranging the formula
We need to find the wavelength (λ), so we rearrange the formula:

\[ \lambda = \frac{c}{\nu} \]

### Step 2: Substituting the values
Now, we substitute the values into the formula. We have:
- \( c = 3 \times 10^{17} \, \text{nm/s} \)
- \( \nu = 6 \times 10^{15} \, \text{s}^{-1} \)

Substituting these values:

\[ \lambda = \frac{3 \times 10^{17}}{6 \times 10^{15}} \]

### Step 3: Simplifying the expression
Now, we simplify the fraction:

\[ \lambda = \frac{3}{6} \times \frac{10^{17}}{10^{15}} = \frac{1}{2} \times 10^{2} = 0.5 \times 100 = 50 \, \text{nm} \]

### Conclusion
The wavelength of the quantum of light with a frequency of \( 6 \times 10^{15} \, \text{s}^{-1} \) is **50 nm**.