Question

Question #2c5a4

Answer 1

`E_2-E_1=DeltaE=hnu=(2pi^2mZ^2e^4K^2)/h^2[1/n_1^2-1/n_2^2]`

`DeltaE=hnu`
`rArr` 3x`10^-19`=[(6.626x`10^-34`)x(3x`10^8`)]/`lambda`

so `lambda`=6.626x`10^-7`m=6626 angstrom

IN DETAIL:
`nu=(2pi^2mZ^2e^4K^2)/h^3[1/n_1^2-1/n_2^2]`

now we know that C=`nulambda`
so `1/lambda=barnu=(2pi^2mZ^2e^4K^2)/(ch^3)[1/n_1^2-1/n_2^2]`

where `(2pi^2me^4K^2)/(ch^3)=109678cm^-1=R`(Rydberg's constant)or 1.09x`10^-7m^-1`

so our final expression looks like this:
`barnu=1/lambda=RZ^2[1/n_1^2-1/n_2^2]`

ans:

`1/lambda`=109678[1/4-1/9]

`lambda`=1/15354.92=6.51x`10^-5`cm
=6510 angstrom