Respuesta :
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.
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 = [tex]5\times 10^5 J/mol[/tex]
1 Mega Joule = [tex]10^6 J[/tex]
The first ionization energy of 1 Na(g) atom = [tex]E_s=\frac{5\times 10^5 J/mol}{6.022\times 10^{23} mol^{-1}}=8.3028\times 10^{-19} J[/tex]
If we have a photon of wavelength = 500 nm = [tex]5.00\times 10^{-7} m[/tex]
[tex]1 nm = 10^{-9} m[/tex]
[tex]E=\frac{h\times c}{\lambda}[/tex]
E = energy of photon = ?
[tex]\lambda[/tex] = wavelength
h = Planck's constant = [tex]6.63\times 10^{-34}Js[/tex]
c = speed of light = [tex]3\times 10^8m/s[/tex]
[tex]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[/tex]
Energy of the photon = E = [tex]3.978\times 10^{-19} J[/tex]
As we can see that ,[tex]E_s>E[/tex]
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.
