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. 10
B. 25
C. 50
D. 75

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), wavelength (λ), and frequency (ν):

\[ c = λ \cdot ν \]

From this equation, we can rearrange it to solve for wavelength (λ):

\[ λ = \frac{c}{ν} \]

### 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. **Substitute the values into the wavelength formula:**
\[ λ = \frac{3 \times 10^{17} \, \text{nm/s}}{6 \times 10^{15} \, \text{s}^{-1}} \]

3. **Perform the division:**
- First, divide the coefficients:
\[ \frac{3}{6} = 0.5 \]
- Next, divide the powers of ten:
\[ 10^{17} \div 10^{15} = 10^{2} \]

4. **Combine the results:**
\[ λ = 0.5 \times 10^{2} \, \text{nm} = 50 \, \text{nm} \]

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

### Final Answer:
The value closest to the wavelength in nanometers of a quantum of light with a frequency of \( 6 \times 10^{15} \, \text{s}^{-1} \) is **50 nm**.