Consider one `He^+` ion in excited state `(n = 5)`. Which of the following of the following observations will hold true as per the Bohr's model.

Options

A. `10` emission spectral lines will be seen
B. The ionisation energy needed is less than `2 eV`
C. The longest emitted wavelength is less than `10//R(R = "Rydberg's constant")`
D. The electronic separation from the centre of nucleus is more than `6 Å`.

Answer

D

Explanation

(d) A multitude of `He^+` will produce `10` possible emission lines. A single `He^+` can produce maximum `4` lines (not more)
`5 rarr 4 rarr 3 rarr 2 rarr 1`
`E_n = -13.6 (z^2)/(n^2) = -13.6 xx (2^2)/(5^2)`
=`-13.6 xx (4)/(25) = -2.176 eV`
`:. " " IE = + 2.176 eV gt 2eV`
`(1)/(lamda) = RZ^2 [(1)/(n_1^2) -(1)/(n_2^2)]`
`(1)/(lamda) = R.4[(1)/(4^2) -(1)/(5^2)]`
` (1)/(lamda) = 4 R[(9)/(16 xx 25)]`
`(1)/(lamda) = (16 xx 25)/(4 xx 9 xx R) = (100)/(9 R) gt (10)/(R)`
`r_n = 0.53 xx (n^2)/(Z) = 0.53 xx (5^2)/(Z)`
=`6.625 Å gt 6^@ A`.