Chapter 15.10, Problem 1KCP

Write the equation relating the energy of radiation to its wavelength and frequency, and give the SI units for each quantity.

To determine

Write the energy equation of radiation relating to its frequency and wavelength and write their SI units.

Explanation of Solution

Write the energy equation of radiation relating to its wavelength and frequency as follows:

 $\begin{array}{c}\Delta E=h\upsilon \\ =\frac{hc}{\lambda }\end{array}$

Here, energy of radiation is $\Delta E$, Planck's constant is $h$, frequency of radiation is $\upsilon$, speed of light is c and wavelength of radiation is $\lambda$.

Show the SI units for each quantity as in Table (1).

S.No.	Quantities	SI units
1	Energy of radiation $\left(\Delta E\right)$	Joules $\left(\text{J}\right)$
2	Planck's constant $\left(h\right)$	Joules-second $\left(\text{J}\cdot \text{s}\right)$
3	Frequency of radiation $\left(\upsilon \right)$	hertz $\left(\text{Hz}\right)$
4	Speed of light $\left(c\right)$	meters per second $\left(\text{m}/\text{s}\right)$
5	Wavelength of radiation $\left(\lambda \right)$	meters $\left(\text{m}\right)$

The values of Planck constant and speed of light are $6.63\times {10}^{-34}\text{J}\cdot \text{s}$ and $3\times {10}^8\text{m}/\text{s}$ respectively.