Respuesta :
Answer:
The wavelength is 2.27 μm.
The energy is [tex]-8.746\times10^{-20}\ J[/tex]
The frequency is [tex]1.319\times10^{14}\ Hz[/tex]
Explanation:
Given that,
Number of spectral line n=9
Number of spectral line n=6
We need to calculate the wavelength
Using formula of wavelength
[tex]\dfrac{1}{\lambda}=R_{h}(\dfrac{1}{n_{f}^2}+\dfrac{1}{n_{i}^2})[/tex]
Put the value into the formula
[tex]\dfrac{1}{\lambda}=1.097\times10^{7}(\dfrac{1}{36}+\dfrac{1}{81})[/tex]
[tex]\dfrac{1}{\lambda}=440154.320988\ m[/tex]
[tex]\lambda=0.0000022719\ m[/tex]
[tex]\lambda=2.27\times10^{-6}\ m[/tex]
[tex]\lambda=2.27\ \mu m[/tex]
The wavelength is 2.27 μm.
We need to calculate the energy
Using formula of energy
[tex]\Delta E=R_{h}(\dfrac{1}{n_{f}^2}+\dfrac{1}{n_{i}^2})[/tex]
Put the value into the formula
[tex]\Delta E=-2.18\times10^{-18}\times(\dfrac{1}{36}+\dfrac{1}{81})[/tex]
[tex]\Delta E=-8.746\times10^{-20}\ J[/tex]
The energy is [tex]-8.746\times10^{-20}\ J[/tex]
We need to calculate the frequency
Using formula of frequency
[tex]f=\dfrac{\Delta E}{h}[/tex]
Put the value into the formula
[tex]f=\dfrac{8.746\times10^{-20}}{6.62\times10^{-34}}[/tex]
[tex]f=1.319\times10^{14}\ Hz[/tex]
The frequency is [tex]1.319\times10^{14}\ Hz[/tex]
Hence, The wavelength is 2.27 μm.
The energy is [tex]-8.746\times10^{-20}\ J[/tex]
The frequency is [tex]1.319\times10^{14}\ Hz[/tex]
