Question

Do the unit conversions necessary to show that $hc=1240eV\cdot nm$, as stated in the text.

Short answer

The necessary unit conversion is done, and the result is obtained as $hc=1240eV\cdot nm$.

Step-by-step solution

Concept Introduction

The frequency of a sinusoidal wave is the number of full oscillations performed by any wave component in one unit of time. The concept of frequency can be used to understand that if a body is in periodic motion, it has finished one cycle after going through a sequence of experiences or locations and returning to its initial state. As a result, frequency is a term used to indicate how frequently oscillations and vibrations take place.

Information Provided

• Value for $hc$ is: $hc=1240eV\cdot nm$.

Unit Conversions

The value of Planck's constant is–

$h=6.626\times {10}^{-34}Js$

And the speed of light is –

$c=3.00\times {10}^{8}m{s}^{-1}$

Therefore, it can be obtained –

$\begin{array}{r}hc=6.626\times {10}^{-34}Js\times 3.00\times {10}^{8}m{s}^{-1}\\ =1.9878\times {10}^{-25}Jm\end{array}$

It is known that –

$1.00m={10}^{9}nm$and,

$1.00J=6.242\times {10}^{18}eV$

Hence, it is obtained that –

­$\begin{array}{r}hc=1.9878\times {10}^{-25}Js\times {\displaystyle \frac{6.242\times {10}^{18}eV}{1.00J}}\times {\displaystyle \frac{{10}^{9}nm}{1.00m}}\\ =1240eV\cdot nm\end{array}$

Therefore, it is proved that $hc=1240eV\cdot nm$.