The first ionization energy of na(g) is 0.50 mj/mole. can a photon with a wavelength of 500 nm ionize a sodium atom? explain.

              No, a photon with a wavelength of 500 nm can't  ionize a sodium atom.

Step 1: Find out Energy of given wavelength:

The relation between wavelength and frequency is as follow,

                                                        υ = c / λ

where

           υ = frequency = ?

           c = velocity of light = 3.0 × 10⁸ ms⁻¹

           λ = wavenumber = 500 nm = 500 × 10⁻⁹ m

Putting the given values,

                                 υ = 3.0 × 10⁸ ms⁻¹ / 500 × 10⁻⁹ m

                                 υ = 6.0 × 10¹⁴ s⁻¹

Also we know that,

                                                        E = h υ

Where;

           E  =  Energy

           h  =  Plank's Constant  =  6.6262 × 10⁻³⁴ Js

Putting value of frequency,

                                 E = 6.6262 × 10⁻³⁴ Js × 6.0 × 10¹⁴ s⁻¹

                                 E = 3.97 × 10⁻¹⁹ J

Step 2: Compare given energy and calculated energy:

As we know,

                                          0.5 mJ  =  500000 J

Also,

                                     500000 J  >  3.97 × 10⁻¹⁹ J

                           The energy of calculated wavelength of photon is less than 0.5 mJ hence, it is unable to ionize sodium atom.

No, a photon with a wavelength of 500 nm cannot ionize a sodium atom. This is because energy of the photon is less than the energy required to ionize a single gaseous sodium atom.

Explanation:

The first ionization energy of Na(g) is 0.50 MJ/mole =

1 Mega Joule =

The first ionization energy of 1 Na(g) atom =

If we have a photon of wavelength = 500 nm =

E = energy of photon = ?

= wavelength

h = Planck's constant =

c = speed of light =

Energy of the photon = E =

As we can see that ,

Photon of this wavelength will not able to ionize the sodium atom.This is because energy of the photon is less than the energy required to ionize a single gaseous sodium atom.

A photon with a wavelength of 500 nm cannot ionize a sodium atom.

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