Consider one He^+ ion is in excited state (n = 5) . Which of the … - Vidyadip

MCQ

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

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 constant)
✓
The electronic separation from the centre of nucleus is more than $6\,\mathop A\limits^o $

✓

Answer

Correct option: D.

The electronic separation from the centre of nucleus is more than $6\,\mathop A\limits^o $

d
One $\mathrm{He}^{+}$ ion, $\mathrm{n}=5$

Maximum lines $=4$

$I.E.$ $=\frac{54.4}{25}=2.176 \,\mathrm{eV}$

$\frac{1}{\lambda}=\mathrm{R} \times 2^{2}\left(\frac{1}{4^{2}}-\frac{1}{5^{2}}\right)$

$=R \times 4^{2} \times \frac{9}{4^{2} \times 5^{2}}$

$ \lambda =\frac{25}{9 \mathrm{R}} $

$ \mathrm{r}_{5}=0.529 \times \frac{5^{2}}{2} =0.529 \times \frac{25}{2} $

$=6.613 \,\mathop A\limits^o $

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