Talamancoeb

2021-12-19

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.

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
$E=\frac{6.626×{10}^{-34}×3×{10}^{8}}{5.03×{10}^{-7}}J$
$E=\frac{19.878×{10}^{-19}}{5.03}$
$E=3.95×{10}^{-19}J$

nick1337

A) The wavelength of red light from a helium-neon laser is 632.8 nm.
The formula to calculate the frequency of electromagnetic radiation is:
$f=\frac{c}{\lambda }$ where $f$ is the frequency, $c$ is the speed of light, and $\lambda$ is the wavelength.
Substituting the given values:
$f=\frac{3.00×{10}^{8}\phantom{\rule{0.167em}{0ex}}\text{m/s}}{632.8×{10}^{-9}\phantom{\rule{0.167em}{0ex}}\text{m}}$
Simplifying the expression:
$f=\frac{3.00}{632.8}×{10}^{17}\phantom{\rule{0.167em}{0ex}}\text{Hz}$
Rounding the result to three significant figures:
$f=4.74×{10}^{14}\phantom{\rule{0.167em}{0ex}}\text{Hz}$
Therefore, the frequency of red light with a wavelength of 632.8 nm is $4.74×{10}^{14}\phantom{\rule{0.167em}{0ex}}\text{Hz}$.
B) The wavelength of maximum solar radiation is 503 nm.
Using the same formula as before:
$f=\frac{3.00×{10}^{8}\phantom{\rule{0.167em}{0ex}}\text{m/s}}{503×{10}^{-9}\phantom{\rule{0.167em}{0ex}}\text{m}}$
Simplifying:
$f=\frac{3.00}{503}×{10}^{17}\phantom{\rule{0.167em}{0ex}}\text{Hz}$
Rounding to three significant figures:
$f=5.97×{10}^{14}\phantom{\rule{0.167em}{0ex}}\text{Hz}$
Hence, the frequency of radiation with a wavelength of 503 nm is $5.97×{10}^{14}\phantom{\rule{0.167em}{0ex}}\text{Hz}$.
C) The wavelength used in medical X-rays is 0.0520 nm.
Using the same formula:
$f=\frac{3.00×{10}^{8}\phantom{\rule{0.167em}{0ex}}\text{m/s}}{0.0520×{10}^{-9}\phantom{\rule{0.167em}{0ex}}\text{m}}$
Simplifying:
$f=\frac{3.00}{0.0520}×{10}^{17}\phantom{\rule{0.167em}{0ex}}\text{Hz}$
Rounding to three significant figures:
$f=5.77×{10}^{18}\phantom{\rule{0.167em}{0ex}}\text{Hz}$
Therefore, the frequency of X-rays with a wavelength of 0.0520 nm is $5.77×{10}^{18}\phantom{\rule{0.167em}{0ex}}\text{Hz}$.

Don Sumner

A) To calculate the frequency of a wavelength, we can use the formula:
$\text{Frequency}=\frac{c}{\lambda }$ where $c$ is the speed of light and $\lambda$ is the wavelength.
For a wavelength of 632.8 nm:
$\text{Frequency}=\frac{3.00×{10}^{8}\phantom{\rule{0.167em}{0ex}}\text{m/s}}{632.8×{10}^{-9}\phantom{\rule{0.167em}{0ex}}\text{m}}$
B) For a wavelength of 503 nm:
$\text{Frequency}=\frac{3.00×{10}^{8}\phantom{\rule{0.167em}{0ex}}\text{m/s}}{503×{10}^{-9}\phantom{\rule{0.167em}{0ex}}\text{m}}$
C) For a wavelength of 0.0520 nm:
$\text{Frequency}=\frac{3.00×{10}^{8}\phantom{\rule{0.167em}{0ex}}\text{m/s}}{0.0520×{10}^{-9}\phantom{\rule{0.167em}{0ex}}\text{m}}$
Now, let's calculate the frequencies:
A) For 632.8 nm:
Frequency $=\frac{3.00×{10}^{8}}{632.8×{10}^{-9}}$ Hz
B) For 503 nm:
Frequency $=\frac{3.00×{10}^{8}}{503×{10}^{-9}}$ Hz
C) For 0.0520 nm:
Frequency $=\frac{3.00×{10}^{8}}{0.0520×{10}^{-9}}$ Hz

Do you have a similar question?