Question

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

• A. 10 emission spectral lines will be seen
• B. The ionisation energy needed is less than 2eV
• 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 1

Answer: (D)

The electronic separation from the centre of nucleus is more than 6 Å

Answer 2

A multitude of He⁺ will produce 10 possible

emission lines. A single He⁺ can produce maximum

4 lines (not more)

5 ¾¾® 4 ¾¾® 3 ¾¾® 2 ¾¾® 1

E_n = – 13.6 $\frac{z^{2}}{n^{2}}$ = – 13.6 × $\frac{2^{2}}{5^{2}}$ = – 13.6 × $\frac{4}{25}$

= – 2.176 eV

\ I.E = + 2.176 eV > 2eV

$\frac{1}{\lambda} = RZ^{2}\left\lbrack \frac{1}{n_{1}^{2}}–\frac{1}{n_{2}^{2}} \right\rbrack$

$\frac{1}{\lambda} = R.4\left\lbrack \frac{1}{4^{2}}–\frac{1}{5^{2}} \right\rbrack$

$\frac{1}{\lambda} = 4R\left\lbrack \frac{9}{16 \times 25} \right\rbrack$

$\frac{1}{\lambda} = \frac{16 \times 25}{4 \times 9 \times R} = \frac{100}{9R} > \frac{10}{R}$r_n = 0.53 ×$\frac{n^{2}}{Z} = 0.53 \times \frac{5^{2}}{Z}$

= 6.625 Å > 6°A