Question

The values of Planck's constant is 6.63 × 10\(^{-34}\) J·s. The velocity of light is 3 × 10\(^{8}\) m/s. Which value is closest to the wavelength in nanometers of a quantum of light with frequency of \( 8 \times 10^{15} \, \text{s}^{-1} \)?

• A. \( 5 \times 10^{-18} \)
• B. \( 4 \times 10^{-10} \)
• C. \( 3 \times 10^{7} \)
• D. \( 2 \times 10^{-15} \)

Hint:

The wavelength of light can be calculated using the formula \( \lambda = \frac{c}{f} \).

Answer 1

The Correct Option is B

Step 1: Use the formula for the wavelength.
The wavelength \( \lambda \) is given by: \[ \lambda = \frac{c}{f} \] where \( c \) is the speed of light and \( f \) is the frequency.
Step 2: Calculate the wavelength.
Substituting the values, we get the wavelength \( \lambda = \frac{3 \times 10^{8}}{8 \times 10^{15}} \approx 4 \times 10^{-10} \, \text{m} \), or \( 4 \times 10^{-9} \, \text{nm} \).
Final Answer: \[ \boxed{4 \times 10^{-10} \, \text{m}} \]