A `H-`like species emitted a photon corresponding to the first line of Lyman series. The photon liberated a photoelectron from `He^(+)` ion in ground state. The de-brogile wavelength of the photoelectron is `2Å` . Select the correct statement (s).

Options

A. Atomic number of `H-`like species is `2`.
B. Atomic number of `H-`like species is `3`.
C. Kinetic energy photonelectron is `27.5 eV`
D. Kinetic energy of photonelectron is `37.5 eV`

Answer

B, D

Explanation

`lambda_(A) = sqrt((150)/(V)) rArr 2 = sqrt((150)/(V))`
`V = 37.5 V`
`K.E.` of photoelectron `= 37.5 eV`
Amount of energy required to liberated electron `= 54.5 eV`
Total energy of photon `= 54.4 + 37.5 = 91.9 eV`
`91.9 = 13.6Z^(2)((1)/(1^(2)) - (1)/(2^(2)))` or `Z = 3`