Question

a. What is the wavelength (in nm) of light having a frequency of 8.5 × 10^13 Hz?
b. What is the frequency (in Hz) of light having a wavelength of 8.78 × 10^2 nm?

Answer 1

Answer:

a. $\lambda = 3529nm$

b. $\nu = 3.416x10^{14}Hz$

Explanation:

The know the frequency and wavelength it can be used the following equation:

$c = \nu \cdot \lambda$ (1)

Where c is the speed of light, $\nu$ is the frequency and $\lambda$ is the wavelength.

a. What is the wavelength (in nm) of light having a frequency of $8.5 x10^{13} Hz$?

The speed of light in vacuum has a value of $3x10^{9}m/s$ and in nanometers, $3x10^{17}nm/s$

Then, $\lambda$ can be isolated from equation 1.

$\lambda = \frac{c}{\nu}$  (2)

$\lambda = \frac{3x10^{17}nm/s}{8.5x10^{13}Hz}$

But $1Hz = s^{-1}$

$\lambda = \frac{3x10^{17}nm/s}{8.5x10^{13}s^{-1}}$

$\lambda = 3529nm$

b. What is the frequency (in Hz) of light having a wavelength of $8.78 x10^{2} nm$

$\nu = \frac{c}{\lambda}$ (3)

Notice that it is necessary to express the wavelength in units of meters.

$\lambda = 8.78x10^{2} nm . \frac{1m}{1x10^{9}nm}$ ⇒ $8.78x10^{-7}m$

Finally, equation 3 can be used.

$\nu = \frac{3x10^{8}m/s}{8.78x10^{-7}m}$

$\nu = 3.416x10^{14}s^{-1}$

$\nu = 3.416x10^{14}Hz$