The value of Planck's constant is 6.63 × 10-34 Js. The speed of light is 3 x 1017 nm s-1. Which value is closest to the wavelength in nanometer of a quantum of light with frequency of 6 x 1015 s-1?
- 10
- 25
- 50
- 75
The Correct Option is C
Solution and Explanation
To determine the wavelength of a quantum of light given its frequency, we can use the fundamental wave equation that relates the speed of light (c), frequency (\nu), and wavelength (\lambda):
c = \lambda \nu
In this equation, \nu is given as 6 \times 10^{15} \text{ s}^{-1}, and we know the speed of light c is 3 \times 10^{17} \text{ nm s}^{-1}.
Rearranging the equation to solve for wavelength \lambda:
\lambda = \frac{c}{\nu}
Substituting the known values:
\lambda = \frac{3 \times 10^{17} \text{ nm s}^{-1}}{6 \times 10^{15} \text{ s}^{-1}}
Solve for \lambda:
\lambda = 0.5 \times 10^2 \text{ nm} = 50 \text{ nm}
Thus, the closest value to the wavelength of a quantum of light with a frequency of 6 \times 10^{15} \text{ s}^{-1} is 50 nm.
Therefore, the correct option is 50.
