Answer:
The energy required is 1.634×[tex]10^{-18}[/tex]J, the wavelength is 1.215×[tex]10^{-7}[/tex]m, and the kind of electromagnetic radiation is the ultraviolet radiation.
Explanation:
In the question above, the initial level [tex]n_{initial}[/tex] = 1, and [tex]n_{final}[/tex] = 2. Then, we use Rydberg's equation to calculate the wavelength of the light absorbed by the atom during the transition.
1/wavelength = R([tex]\frac{1}{n_{initial} ^{2} } -\frac{1}{n_{final} ^{2} }[/tex])
where:
R is the Rydberg's constant which is equal to 1.0974×[tex]10^{7}[/tex] [tex]m^{-1}[/tex]
Therefore,
1/wavelength = 1.0974×[tex]10^{7}[/tex] [tex]m^{-1}[/tex]×([tex]\frac{1}{1 ^{2} } -\frac{1}{2^{2} }[/tex]) = 1.0974×[tex]10^{7}[/tex] [tex]m^{-1}[/tex]×[tex](\frac{1}{4}-\frac{1}{1} )[/tex] = (-) 0.8228*10^{7}
Thus,
wavelength = [tex]\frac{1}{0.8228*10^{7}}[/tex] = 1.215*[tex]10^{-7} \frac{1}{m}[/tex]
The energy required (E) can be calculated using:
E = h*c/wavelength
where:
h is the Planck's constant = 6.626*[tex]10^{-34} J.s[/tex]
c is the speed of light = 299,792,458 m/s
Therefore,
E = 6.626*[tex]10^{-34} J.s[/tex]*299,792,458 m/s÷ 1.215*[tex]10^{-7} \frac{1}{m}[/tex] = 1.634*[tex]10^{-18} J[/tex]
The kind of electromagnetic radiation used is is the ultraviolet radiation. This is the type of electromagnetic radiation with wavelength between 10 nm and 400 nm
