Respuesta :
Answer:
The wavelength of light is 2772 μm.
Explanation:
Given that,
Frequency = 1580 cm⁻¹
Higher state =5
Lower state = 2
We need to calculate the energy for n = 5
Using formula of energy
[tex]E_{5}=hf(n+\dfrac{1}{2})[/tex]
Put the value into the formula
[tex]E_{5}=6.63\times10^{-34}\times1580\times10^{-2}(5+\dfrac{1}{2})[/tex]
[tex]E_{5}=5.76147\times10^{-32}\ J[/tex]
For n = 2,
[tex]E_{2}=6.63\times10^{-34}\times1580\times10^{-2}(2+\dfrac{1}{2})[/tex]
[tex]E_{2}=2.61885\times10^{-32}\ J[/tex]
We need to calculate the energy
Using formula of energy
[tex]E=E_{5}-E_{2}[/tex]
Put the value into the formula
[tex]E=(5.79623-2.63465)\times10^{-32}[/tex]
[tex]E=3.14262\times10^{-32}\ J[/tex]
We need to calculate the wavelength
Using formula of wavelength
[tex]\lambda=\dfrac{h}{\sqrt{2mE}}[/tex]
Put the value into the formula
[tex]\lambda=\dfrac{6.63\times10^{-34}}{\sqrt{2\times9.1\times10^{-31}\times3.14262\times10^{-32}}}[/tex]
[tex]\lambda=0.00277224685446\ m[/tex]
[tex]\lambda=2772\times10^{-6}\ m[/tex]
[tex]\lambda =2772\ \mu m[/tex]
Hence, The wavelength of light is 2772 μm.
