Determine the minimum wavelength that hydrogen in its ground state can obsorb. What would be the next smaller wavelength that would work?

Options

A. `133 nm`
B. `13.3 nm`
C. `10.3 nm`
D. `103 nm`

Answer

D

Explanation

When wavelength is maximum, the energy is maximum. Hence, this is from the ground state to the first excited state, for which the energy is `13.6 eV - 3.4 eV = 10.2 eV`
hence, the required wavelength is `122 nm`
The next possibility is to jump from the ground state to the second excited state which requires `=m 13.6 xx 1.5 = 12.1 eV`.
Hence, it correcponding to a wavelength
`lambda = ( c)/(v) = (hc)/(E_(3) - E_(1)) = ((6.63 xx 10^(-34)) xx(3 xx 10^(8)))/((12.1) xx (1.6 xx 10^(-19))) = 103 nm`