Monochromatic radiation of wavelength `lambda` are incident on a hydrogen sample in ground state. Hydrogen atoms absorb the light and subsequently emit radiations of 10 different wavelength . The value of `lambda` is nearly :

Explanation

From nth energy state a total of `(n(-1))/(2)` lines are emitted.
`:. " " (n(n-1))/(2)=10or n=5`
Further , `" " E_(n)=(E_(1))/(n^(2))`
`:." " E_(5)=(-13.6)/((5^(2)))=-0.544 eV`
The energy needed to take a hydrogen atom form its ground state to n=5 is
`DeltaE=E_(5)-E_(1)`
`=-0.54-(-13.6)`
=13.06 eV
The corresponding wavelength of light,
`lambda=(12375)/(DeltaE)Å=(12375)/(13.06)=947.5Å`