# Calculate the frequency of each of the following wavelengths of electr

Calculate the frequency of each of the following wavelengths of electromagnetic radiation.
A) 632.8 nm (wavelength of red light from a helium-neon laser) Express your answer using three significant figures.
C) 0.0520 nm (a wavelength used in medical X rays) Express your answer using three significant figures.
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Cassandra Ramirez
Step 1
Given: We have to calculate the frequency of each of the following wave length of electromagnetic radiation.
A) Wave length $\left(\lambda \right)=632.8nm=632.8×{10}^{-9}m$.
Velocity $\left(c\right)=3×{10}^{8}\frac{m}{s}$
Frequency $\left(\nu \right)=?$
Now, $C=\lambda \nu$
$⇒\nu =\frac{c}{\lambda }=\frac{3×{10}^{8}}{632.8×{10}^{-9}}=4.74×{10}^{14}Hz$.
Hence, the frequency is $4.74×{10}^{14}Hz$
B) wave length $\left(\lambda \right)=503nm=503×{10}^{-9}m$
velocity $\left(c\right)=3×{10}^{8}\frac{m}{s}$
Frequency $\left(\nu \right)=?$
Now, $\nu =\frac{C}{\lambda }=\frac{3×{10}^{8}}{503×{10}^{-9}}=5.96×{10}^{14}Hz$
Hence, the frequency is $5.96×{10}^{14}Hz$
c) wave length $\left(\lambda \right)=0.052nm=0.052×{10}^{-9}m$
velocity $\left(c\right)=3×{10}^{8}\frac{m}{s}$
Frequency $\left(\nu \right)=?$
Now, $\nu =\frac{c}{\lambda }=\frac{3×{10}^{8}}{0.052×{10}^{-9}}=5.77×{10}^{18}Hz$
Hence, the frequency is $5.77×{10}^{18}Hz$

Jenny Sheppard
b) We know energy of photon is given by:
$E=h\nu =\frac{hc}{\lambda }$
where, $h=\text{planles constant}$
$c=\text{speed of light}$
$\lambda =\text{wave length}$
$\nu =\text{frequency}$
$h=6.626×{10}^{-34}Js$
$c=3×{10}^{8}ms$ [on $2.998×{10}^{8}\frac{m}{s}$]
$\lambda =503nm=5.03×{10}^{-7}m$
Putting the values
$E=\frac{6.626×{10}^{-34}×3×{10}^{8}}{5.03×{10}^{-7}}J$
$E=\frac{19.878×{10}^{-19}}{5.03}$
$E=3.95×{10}^{-19}J$