Question

What is the wavelength of a monochromatic light beam, where the photon energy is 2.70 × 10^−19 J? (h = 6.63 ×10^−34 J⋅s, c = 3.00 × 10^8 m/s, and 1 nm = 10^−9 m)

Answer 1

Wavelength = 736.67 nm

Step-by-step explanation:

Given

Energy of the photon = 2.70 × 10⁻¹⁹ J

Considering:

`Energy=h* frequency`

where, h is Plank's constant having value as 6.63 x 10⁻³⁴ J.s

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

So, Formula for energy:

`Energy=h* \frac {c}{\lambda}`

Energy = 2.70 × 10⁻¹⁹ J

c = 3×10⁸ m/s

h = 6.63 x 10⁻³⁴ J.s

Thus, applying in the formula:

`2.70* 10^(-19)=6.63* 10^(-34)* \frac {3* 10^8}{\lambda}`

Wavelength = 736.67 × 10⁻⁹ m

1 nm = 10⁻⁹ m

So,

Wavelength = 736.67 nm