Question

Convert 850 nm wavelength into frequency, eV, wavenumber, joules and ergs.

Answer 1

Frequency =
`3.5294* 10^(14)s^(-1)`

Wavenumber =
`1.1765* 10^6m^(-1)`

Energy =
`2.3365* 10^(-19)J`

Energy = 1.4579 eV

Energy =
`2.3365* 10^(-12)erg`

Step-by-step explanation:

As we are given the wavelength = 850 nm

conversion used :
`(1nm=10^(-9)m)`

So, wavelength is
`850* 10^(-9)m`

The relation between frequency and wavelength is shown below as:

`Frequency=(c)/(Wavelength)`

Where, c is the speed of light having value =
`3* 10^8m/s`

So, Frequency is:

`Frequency=(3* 10^8m/s)/(850* 10^(-9)m)`

`Frequency=3.5294* 10^(14)s^(-1)`

Wavenumber is the reciprocal of wavelength.

So,

`Wavenumber=(1)/(Wavelength)=(1)/(850* 10^(-9)m)`

`Wavenumber=1.1765* 10^6m^(-1)`

Also,

`Energy=h* frequency`

where, h is Plank's constant having value as
`6.62* 10^(-34)J.s`

So,

`Energy=(6.62* 10^(-34)J.s)* (3.5294* 10^(14)s^(-1))`

`Energy=2.3365* 10^(-19)J`

Also,

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

So,

`Energy=(2.3365* 10^(-19))* (6.24* 10^(18)eV)`

`Energy=1.4579eV`

Also,

`1J=10^7erg`

So,

`Energy=(2.3365* 10^(-19))* 10^7erg`

`Energy=2.3365* 10^(-12)erg`