Balmer gives an equation for wavelength of visible radition of `H^(-)` spectrum as `lambda=(kn^(2))/(n^(2)-4)`.The value of `k` in terms of Rydberg's constant `R` is

Options

A. `R`
B. `4R`
C. `R/4`
D. `4/R`

Answer

D

Explanation

form Bohr's theory of atomic spectra,
`1/lambda=RZ^(2)(1/(n_(1)^(2))-1/(n_(2)^(2)))`
for hydrogen atom, Z=1 and for visible spectrum, `n_(1)=2`
` :. 1/lambda=R(1/(2^(2))-1/(n^(2)))=R((n^(2)-4)/(4n^(2)))`
or `lambda=(4n^(2))/(R(n^(2)-4)).......(i)`
Given, `lambda=(kn^(2))/(n^(2)-4)........(ii)`
form (i) and (ii)
`(kn^(2))/(n^(2)-4)=(4n^(2))/(R(n^(2)-4)) or k=4/R`