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A beam of light from a sodium street lamp is found to have a frequency of 5.09 x 1014 Hz. What is the wavelength?

physics
Guest Jun 12, 2015

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 #2
avatar+91024 
+10

A beam of light from a sodium street lamp is found to have a frequency of 5.09 x 1014 Hz. What is the wavelength?

Hz is wavelengths per sec

so I use the units in a rather unusual way. I am sure others would use a formua.

we have

 

 $$\\frequency =\frac{5.09*10^{14}\;\;\lambda}{second}\qquad speed\;of\;light=\frac{299792458\;m}{sec}\qquad we\;want\;\; \frac{m}{\lambda}\\\\
\frac{299792458\;m}{sec}\times \frac{sec}{5.09*10^{14}\;\;\lambda}\qquad $The seconds cancel out$\\\\
=\frac{299792458\;m}{5.09*10^{14}\;\;\lambda}$$

 

$${\frac{{\mathtt{299\,792\,458}}}{\left({\mathtt{5.09}}{\mathtt{\,\times\,}}{{\mathtt{10}}}^{{\mathtt{14}}}\right)}} = {\mathtt{0.000\: \!000\: \!588\: \!983\: \!218\: \!1}}$$

 

So the wavelength is    $$\approx 589*10^{-9}\;\;metres = 589\;nanometres$$    

Melody  Jun 12, 2015
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2+0 Answers

 #1
avatar+18712 
+10

A beam of light from a sodium street lamp is found to have a frequency of 5.09 x 1014 Hz. What is the wavelength?

 

$$\boxed{\; c = f\cdot \lambda \qquad \text{ or }\qquad \lambda=\dfrac{c}{f} \qquad \text{ or }\qquad f=\dfrac{c}{\lambda} \qquad \begin{array}{rcl} c &=& \small{\text{ speed of light in vacuum }} \\\lambda &=& \small{\text{ wavelength }} \\ f &=& \small{\text{ wave's frequency }}\end{Array}\; }$$

 

$$\small{\text{$
\begin{array}{rclcc} \lambda &=& \dfrac{c}{f} \quad & \quad c = 299\,792\,458 ~ \mathrm{\dfrac{m}{s}} \quad & \quad
f = 5.09 \cdot 10^{14} ~ \mathrm{ Hz } \\\\
\lambda &=& \dfrac{ 299\,792\,458 ~ \mathrm{\dfrac{m}{s}} }{ 5.09\cdot 10^{14} ~ \mathrm{ Hz } } \\\\
\lambda &=& \dfrac{ 2.99\,792\,458\cdot 10^{8} ~ \mathrm{\dfrac{m}{s}} }{5.09\cdot 10^{14} ~ \mathrm{\dfrac{1}{s}} } \\\\
\lambda &=& \dfrac{ 2.99\,792\,458 }{5.09}\cdot 10^{8}\cdot 10^{-14} ~ \mathrm{ m } \\\\
\lambda &=& 0.58898321807\cdot 10^{-6} ~ \mathrm{ m } \\\\
\lambda &=& 588.98321807\cdot 10^{-3} \cdot 10^{-6} ~ \mathrm{m} \\\\
\lambda &=& 588.98321807\cdot 10^{-9} ~ \mathrm{m} \\\\
\lambda &=& 588.98321807 ~ \mathrm{nm}
\end{array}$}}$$

 

heureka  Jun 12, 2015
 #2
avatar+91024 
+10
Best Answer

A beam of light from a sodium street lamp is found to have a frequency of 5.09 x 1014 Hz. What is the wavelength?

Hz is wavelengths per sec

so I use the units in a rather unusual way. I am sure others would use a formua.

we have

 

 $$\\frequency =\frac{5.09*10^{14}\;\;\lambda}{second}\qquad speed\;of\;light=\frac{299792458\;m}{sec}\qquad we\;want\;\; \frac{m}{\lambda}\\\\
\frac{299792458\;m}{sec}\times \frac{sec}{5.09*10^{14}\;\;\lambda}\qquad $The seconds cancel out$\\\\
=\frac{299792458\;m}{5.09*10^{14}\;\;\lambda}$$

 

$${\frac{{\mathtt{299\,792\,458}}}{\left({\mathtt{5.09}}{\mathtt{\,\times\,}}{{\mathtt{10}}}^{{\mathtt{14}}}\right)}} = {\mathtt{0.000\: \!000\: \!588\: \!983\: \!218\: \!1}}$$

 

So the wavelength is    $$\approx 589*10^{-9}\;\;metres = 589\;nanometres$$    

Melody  Jun 12, 2015

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