Question

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

Answer 1

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

(b) The wavelength of blue light is
`4* 10^(-5)cm`

Step-by-step explanation:

The relation between the energy and frequency is:

`Energy=h* Frequency`

where,

h = Plank's constant =
`6.626* 10^(-34)J.s`

Given :

Frequency =
`670THz=670* 10^(12)s^(-1)`

Conversion used :

`1THz=10^(12)Hz\\1Hz=1s^(-1)\\1THz=10^(12)s^(-1)`

So,

`Energy=(6.626* 10^(-34)J.s)* (670* 10^(12)s^(-1))`

`Energy=4.44* 10^(-19)J`

Also,

`1J=6.24* 10^(18)eV`

So,

`Energy=(4.44* 10^(-19))* (6.24* 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=(c)/(Wavelength)`

Where,

c = the speed of light =
`3* 10^8m/s`

Frequency =
`670* 10^(12)s^(-1)`

So, Wavelength is:

`670* 10^(12)s^(-1)=(3* 10^8m/s)/(Wavelength)`

`Wavelength=(3* 10^8m/s)/(670* 10^(12)s^(-1))=4* 10^(-7)m=4* 10^(-5)cm`

Conversion used :
`1m=100cm`

The wavelength of blue light is
`4* 10^(-5)cm`