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)

Wavelength = 736.67 nm

Explanation:

Given

Energy of the photon = 2.70 × 10⁻¹⁹ J

Considering:

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 = 2.70 × 10⁻¹⁹ J

c = 3×10⁸ m/s

h = 6.63 x 10⁻³⁴ J.s

Thus, applying in the formula:

Wavelength = 736.67 × 10⁻⁹ m

1 nm = 10⁻⁹ m

So,

Wavelength = 736.67 nm