Question

Determine the a) energy (in eV) and b) wavelength (in cm) corresponding to blue light of frequency 670 THz

Answer 1

Answer :

(a) The energy of blue light (in eV) is 2.77 eV

(b) The wavelength of blue light is $4\times 10^{-5}cm$

Explanation:

The relation between the energy and frequency is:  

$Energy=h\times Frequency$

where,

h = Plank's constant = $6.626\times 10^{-34}J.s$

Given :

Frequency = $670THz=670\times 10^{12}s^{-1}$

Conversion used :

$1THz=10^{12}Hz\\1Hz=1s^{-1}\\1THz=10^{12}s^{-1}$

So,  

$Energy=(6.626\times 10^{-34}J.s)\times (670\times 10^{12}s^{-1})$

$Energy=4.44\times 10^{-19}J$

Also,  

$1J=6.24\times 10^{18}eV$

So,  

$Energy=(4.44\times 10^{-19})\times (6.24\times 10^{18}eV)$

$Energy=2.77eV$

The energy of blue light (in eV) is 2.77 eV

The relation between frequency and wavelength is shown below as:

$Frequency=\frac{c}{Wavelength}$

Where,

c = the speed of light = $3\times 10^8m/s$

Frequency = $670\times 10^{12}s^{-1}$

So, Wavelength is:

$670\times 10^{12}s^{-1}=\frac{3\times 10^8m/s}{Wavelength}$

$Wavelength=\frac{3\times 10^8m/s}{670\times 10^{12}s^{-1}}=4\times 10^{-7}m=4\times 10^{-5}cm$

Conversion used : $1m=100cm$

The wavelength of blue light is $4\times 10^{-5}cm$