Question

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.

Answer 1

Answer:

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 = $5\times 10^5 J/mol$

1 Mega Joule = $10^6 J$

The first ionization energy of 1 Na(g) atom = $E_s=\frac{5\times 10^5 J/mol}{6.022\times 10^{23} mol^{-1}}=8.3028\times 10^{-19} J$

If we have a photon of wavelength = 500 nm = $5.00\times 10^{-7} m$

$1 nm = 10^{-9} m$

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

E = energy of photon = ?

$\lambda$ = wavelength

h = Planck's constant = $6.63\times 10^{-34}Js$

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

$E=\frac{6.63\times 10^{-34}J s\times 3\times 10^8 m/s}{5.00\times 10^{-7}m}=3.978\times 10^{-19} J$

Energy of the photon = E = $3.978\times 10^{-19} J$

As we can see that ,$E_s>E$

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.

Answer 2

Answer:

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

Explanation:

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

Conclusion:

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