Question

1. calculate the energy and frequency of red light having a wavelength of 6.80 x 10^(-5) cm.
2. the wavelength of green light from a traffic signal is centered at 5.20 x 10^(-5) cm. calculate the frequency.

Explanation:

Step1: Convert wavelength to meters

First, convert the given wavelengths from centimeters to meters. Since $1\ cm = 0.01\ m=1\times10^{- 2}\ m$.
For red - light: $\lambda_{red}=6.80\times10^{-5}\ cm = 6.80\times10^{-7}\ m$
For green - light: $\lambda_{green}=5.20\times10^{-5}\ cm = 5.20\times10^{-7}\ m$

Step2: Calculate the frequency using the formula $c = \lambda

u$
The speed of light $c = 3.00\times10^{8}\ m/s$. From $c=\lambda
u$, we can solve for the frequency $
u=\frac{c}{\lambda}$.
For red - light: $
u_{red}=\frac{3.00\times10^{8}\ m/s}{6.80\times10^{-7}\ m}\approx4.41\times10^{14}\ Hz$
For green - light: $
u_{green}=\frac{3.00\times10^{8}\ m/s}{5.20\times10^{-7}\ m}\approx5.77\times10^{14}\ Hz$

Step3: Calculate the energy of red - light using the formula $E = h

u$
The Planck's constant $h = 6.63\times10^{-34}\ J\cdot s$.
$E_{red}=h
u_{red}=6.63\times10^{-34}\ J\cdot s\times4.41\times10^{14}\ Hz\approx2.92\times10^{-19}\ J$

Answer:

For red - light:
Energy $E\approx2.92\times10^{-19}\ J$, Frequency $
u\approx4.41\times10^{14}\ Hz$
For green - light:
Frequency $
u\approx5.77\times10^{14}\ Hz$