Some instruments differentiate individual quanta of electromagnetic radiation based on their energies. assume such an instrument has been adjusted to detect quanta that have 3.50× 10–16 j of energy. what is the wavelength of the detected radiation? give your answer in nanometers.

There is a relationship between the energy of a photon and its wavelength. This can be expressed as a mathematical equation shown below:

E = hc/λ
where
h is the Planck's constant equal to 6.62607004 × 10⁻³⁴ m² kg / s
c is the speed of light equal to 3× 10⁸ m/s
λ is the wavelength

3.5×10⁻¹⁶ J = (6.62607004 × 10⁻³⁴ m² kg / s)(3× 10⁸ m/s)/λ
Solving for λ,
λ = 56.8×10⁻⁹ m or 56.8 nm