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Find the energy (in kJ) of a wave with a wavelength of 507 nm.

Question:

Find the energy (in kJ) of a wave with a wavelength of 507 nm.

Energy's Formula and Units:


The formula for the required energy of wave measured in joules for this problem in terms of the wavelength of the wave {eq}\lambda {/eq} is shown below:

{eq}\displaystyle E=\frac{hc}{\lambda} {/eq}, where,

  • "h" is Planck's constant and it is equal to {eq}6.63\times 10^{-34}\ J\cdot s {/eq}.
  • "c" is the value of the speed of the light and its standard value is {eq}3\times 10^8\ m/s {/eq}.

The relation between the units of the energy of the wave is:

{eq}\rm 1\ joule=\frac{1}{1000}\ kilojoules {/eq}

Answer and Explanation:


The given value is:

  • The value of the wavelength of the wave is {eq}\lambda =507\ nm {/eq}.

The value of the above wavelength in meters is:

{eq}\begin{align*} \displaystyle \lambda& =\rm 507\ nm\times \frac{10^{-9}\ m}{1\ nm}\\ & =\displaystyle \rm 507\times 10^{-9}\ m\\ \end{align*} {/eq}


Substituting all the above values with the standard values in the formula of the energy and simplifying it, we get:

{eq}\begin{align*} \displaystyle E&=\frac{6.63\times 10^{-34}(3\times 10^8)}{507\times 10^{-9}}\\ \displaystyle E&=\frac{19.89\times 10^{-26}}{507\times 10^{-9}}\\ \displaystyle E&=3.92\times 10^{-19}\ J\\ \end{align*} {/eq}


Converting the unit of the above value in kilojoule, we get:

{eq}\begin{align*} \displaystyle E&=3.92\times 10^{-19}\ J\times \frac{1\ kJ}{1000\ J}\\ &=3.92\times 10^{-19}\times 10^{-3}\ kJ\\ &=\boxed{\rm 3.92\times 10^{-22}\ kJ}\\ \end{align*} {/eq}


Learn more about this topic:

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What is Energy Conservation? - Definition, Process & Examples

from ICSE Environmental Science: Study Guide & Syllabus

Chapter 1 / Lesson 6
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