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

Answer: (C)

4×101

Answer 2

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.