Question

The value of Planck's constant is 6.63×10^–34Js. The velocity of light is 3.0×10⁸ ms^–1. Which value is closest to the wavelength in nanometers of a quantum of light with a frequency of 8×10¹⁵ s^–1:

• A. 2×10^–25
• B. 5×10^–18
• C. 4×10¹
• D. 3 ×10⁷

Answer 1

The Correct Option is C

wavelength (λ) = \(\frac{speed\,of\,light(c)}{frequency(\nu)}\)
Given:
Speed of light (c) = 3.0 × 10⁸ m/s
Frequency (ν) = 8 × 10¹⁵ s^(-1)
Now, plug these values into the formula:
λ = \(\frac{3.0\times10^8\,m/s}{8\times10^15s^{(-1)}}\)
λ = \(\frac{3.0\times10^8\,m/s}{8\times10^{15}s^{(-1)}}\) = \(\frac{3.0\times10^8\,m/s}{8\times10^{15}s^{(-1)}}\) = (\(\frac{3.0}{8}\)) × 10^(-7) m
There are 10⁹ nanometers in a meter, so:
λ = [(\(\frac{3.0}{8}\)) × 10^(-7) m] × (10⁹ nm/m)
λ = (\(\frac{3.0}{8}\)) × 10^(-7) × 10⁹ nm
λ = (\(\frac{3.0}{8}\)) × 10² nm
λ = 0.375 × 10² nm
λ = 37.5 nm
So, the closest value of wavelength 37.5 nm is Option (C): 40 x 10¹nm.