The value of Planck's constant is `6.63 xx 10^(-34)Js`. The speed of light is `3xx10^(17)nm s^(-1)`. Which value is the closed to the wavelength in nanometers of a quantum of light with frequency `6 xx 10^(10)s^(-1)`?

Options

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

Explanation

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

\[ c = ν \cdot λ \]

Where:
- \( c \) = speed of light
- \( ν \) = frequency
- \( λ \) = wavelength

### Step-by-Step Solution:

1. **Identify the Given Values**:
- Speed of light, \( c = 3 \times 10^{17} \, \text{nm/s} \)
- Frequency, \( ν = 6 \times 10^{15} \, \text{s}^{-1} \)

2. **Rearrange the Formula**:
To find the wavelength \( λ \), we rearrange the formula:
\[ λ = \frac{c}{ν} \]

3. **Substitute the Values**:
Now, substitute the values of \( c \) and \( ν \) into the rearranged formula:
\[ λ = \frac{3 \times 10^{17} \, \text{nm/s}}{6 \times 10^{15} \, \text{s}^{-1}} \]

4. **Perform the Calculation**:
- First, divide the coefficients:
\[ \frac{3}{6} = 0.5 \]
- Then, divide the powers of ten:
\[ 10^{17} / 10^{15} = 10^{2} \]
- Now combine these results:
\[ λ = 0.5 \times 10^{2} \, \text{nm} = 50 \, \text{nm} \]

5. **Conclusion**:
The wavelength of the quantum of light with the given frequency is \( 50 \, \text{nm} \).

### Final Answer:
The wavelength is closest to **50 nm**.