Question

If a laser light is compose of photons each with an energy of 4.58 × 10−19 J, what is the photon energy of this light in units of nanometers, nm? Report your answer with correct significant figures and correct units.

Answer 1

Answer : The photon energy of this light in units of nanometers, (nm) is, $4.34\times 10^{-2}nm$

Solution :

Formula used :

$E=\frac{h\times c}{\lambda}$

where,

E = energy of photon = $4.58\times 10^{-19}J$

h = Planck's constant = $6.626\times 10^{-34}Js$

c = speed of light = $3\times 10^8m/s$

$\lambda$ = wavelength = ?

Now put all the given values in the above formula, we get:

$4.58\times 10^{-19}J=\frac{(6.626\times 10^{-34}Js)\times (3\times 10^8m/s)}{\lambda}$

$\lambda=4.3017\times 10^{-7}m=434.017\times 10^{-9}m=434.017nm=4.34\times 10^{-2}nm$

conversion used : $(1nm=1\times 10^{-9}m)$

Therefore, the photon energy of this light in units of nanometers, (nm) is, $4.34\times 10^{-2}nm$