Answer:
[tex]410.2 nm[/tex]
Explanation:
We are given that
[tex]n_1=2,n_2=6[/tex]
We have to find the wavelength of laser should you used.
We know that
[tex]\frac{1}{\lambda}=R(\frac{1}{n^2_1}-\frac{1}{n^2_2})[/tex]
Where [tex]R=1.097\times 10^7/m[/tex]=Rydberg constant
[tex]\lambda[/tex]=Wavelength
Using the formula
[tex]\frac{1}{\lambda}=1.097\times 10^7(\frac{1}{2^2}-\frac{1}{6^2})[/tex]
[tex]\frac{1}{\lambda}=1.097\times 10^7(\frac{1}{4}-\frac{1}{36})[/tex]
[tex]\frac{1}{\lambda}=1.097\times 10^7(\frac{9-1}{36}=1.097\times 10^7\times \frac{8}{36}[/tex]
[tex]\frac{1}{\lambda}=\frac{1.097\times 10^7}{4}[/tex]
Using identity:[tex]\frac{1}{a^x}=a^{-x}[/tex]
[tex]\lambda=\frac{4}{1.097}\times 10^{-7}[/tex]=[tex]4.102\times 10^{-7} m[/tex]
1 nm=[tex]10^{-9} m[/tex]
[tex]\lambda=4.102\times 100 \times 10^{-9}=410.2\times 10^{-9} [/tex] m=410.2 nm
Hence, the wavelength of laser=[tex]410.2 nm[/tex]
