Question

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

Answer 1

Frequency = 3.5294×10¹⁴ s⁻¹

Wavenumber = 1.1765×10⁶ m⁻¹

Energy = 2.3365x 10⁻¹⁹ J , 1.4579 eV , 2.3365x 10⁻¹² erg

Step-by-step explanation:

Given the wavelength = 850 nm

1 nm = 10⁻⁹ m

So, wavelength is 850×10⁻⁹ m

The relation between frequency and wavelength is shown below as:

c = frequency × Wavelength

Where, c is the speed of light having value = 3×10⁸ m/s

So, Frequency is:

Frequency = c / Wavelength

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

Frequency = 3.5294×10¹⁴ s⁻¹

Wavenumber is the reciprocal of wavelength.

So,

Wavenumber = 1 / Wavelength = 1 / 850×10⁻⁹ m

Wavenumber = 1.1765×10⁶ m⁻¹

Also,

`Energy=h* frequency`

where, h is Plank's constant having value as 6.62x 10⁻³⁴ J.s

So,

Energy = 6.62x 10⁻³⁴ J.s × 3.5294×10¹⁴ s⁻¹

Energy = 2.3365x 10⁻¹⁹ J

Also,

1 J = 6.24×10¹⁸ eV

So,

Energy = 2.3365x 10⁻¹⁹ × 6.24×10¹⁸ eV

Energy = 1.4579 eV

Also,

1 J = 10⁷ erg

So,

Energy = 2.3365x 10⁻¹⁹ × 10⁷ erg

Energy = 2.3365x 10⁻¹² erg