Question

Some instruments differentiate individual quanta of electromagnetic radiation based on their energies. Assume such an instrument has been adjusted to detect quanta that have 3.00x10^-16 J of energy. What is the wavelength of the detected radiation? In nanometers.

Answer 1

Energy = 3.00 x 10⁶ J

We know that,

E = h c /

Where, E = energy = 3.00 x 10^-16 J

h = plank's constant = 6.626 x 10^-34 Js

c = speed of light = 3.00 x 10⁸ ms^-1

= wavelength = ?

Substituting the above values in the equation E = h c / , we get

3.00 x 10^-16 J = { (6.626 x 10^-34 Js ) (3.00 x 10⁸ ms^-1) } /

= { (6.626 x 10^-34 Js ) (3.00 x 10⁸ ms^-1) } / (3.00 x 10^-16 J)

= 6.626 x 10^-10 m

= (6.626 x 10^-10) x 10⁹ nm

= 6.626 x 10^-1 nm

= 0.6626 nm

= 0.66 nm ( upto 2 significant digits)