# 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}

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} 