Answer:
(a) The energy of the photon is 1.632 x [tex]10^{-8}[/tex] J.
(b) The wavelength of the photon is 1.2 x [tex]10^{-17}[/tex] m.
(c) The frequency of the photon is 2.47 x [tex]10^{25}[/tex] Hz.
Explanation:
Let;
[tex]E_{1}[/tex] = -13.60 ev
[tex]E_{2}[/tex] = -3.40 ev
(a) Energy of the emitted photon can be determined as;
[tex]E_{2}[/tex] - [tex]E_{1}[/tex] = -3.40 - (-13.60)
= -3.40 + 13.60
= 10.20 eV
= 10.20(1.6 x [tex]10^{-9}[/tex])
[tex]E_{2}[/tex] - [tex]E_{1}[/tex] = 1.632 x [tex]10^{-8}[/tex] Joules
The energy of the emitted photon is 10.20 eV (or 1.632 x [tex]10^{-8}[/tex] Joules).
(b) The wavelength, λ, can be determined as;
E = (hc)/ λ
where: E is the energy of the photon, h is the Planck's constant (6.6 x [tex]10^{-34}[/tex] Js), c is the speed of light (3 x [tex]10^{8}[/tex] m/s) and λ is the wavelength.
10.20(1.6 x [tex]10^{-9}[/tex]) = (6.6 x [tex]10^{-34}[/tex] * 3 x [tex]10^{8}[/tex])/ λ
λ = [tex]\frac{1.98*10^{-25} }{1.632*10^{-8} }[/tex]
= 1.213 x [tex]10^{-17}[/tex]
Wavelength of the photon is 1.2 x [tex]10^{-17}[/tex] m.
(c) The frequency can be determined by;
E = hf
where f is the frequency of the photon.
1.632 x [tex]10^{-8}[/tex] = 6.6 x [tex]10^{-34}[/tex] x f
f = [tex]\frac{1.632*10^{-8} }{6.6*10^{-34} }[/tex]
= 2.47 x [tex]10^{25}[/tex] Hz
Frequency of the emitted photon is 2.47 x [tex]10^{25}[/tex] Hz.
