According to Bohr's theory, the electronic energy of hydrogen atom in the nth Bohr's orbit is given by: En =(-21.7 × 10-19/n2) J Calculate the longest wavelength of electron from the third Bohr's orbit of the He+ ion.

Question

According to Bohr's theory, the electronic energy of hydrogen atom in the nth Bohr's orbit is given by: En =(-21.7 × 10-19/n2) J Calculate the longest wavelength of electron from the third Bohr's orbit of the He+ ion. (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

For H-like species, the energy of stationary orbit is expressed as

E (X) = Z^{2} \times E (H)

\Rightarrow

For

H e^{+} (Z = 2)

E = - \frac{4 \times 21.7 \times 1 0 ^{- 19}}{n ^{2}} J

For longest wavelength transition from

3^{rd}

orbit, electron must jump to

4^{th}

orbit and the transition energy can be determined as

Δ; E = + 4 \times 21.7 \times 1 0^{- 19} (\frac{1}{9} - \frac{1}{16}) J = 4.22 \times 1 0^{- 19} J

Also,

∵ Δ; E = \frac{h c}{λ}

∴ λ = \frac{h c}{Δ E} = \frac{6.625 \times 1 0 ^{- 34} \times 3 \times 1 0 ^{8}}{4.22 \times 1 0 ^{- 19}} m

= 471 \times 1 0^{- 9} m = 471 nm

Q. According to Bohr's theory, the electronic energy of hydrogen atom in the nth Bohr's orbit is given by : En​=n2−21.7×10−19​J Calculate the longest wavelength of electron from the third Bohr's orbit of the He+ ion.

Q. According to Bohr's theory, the electronic energy of hydrogen atom in the nth Bohr's orbit is given by :
$E_{n} = \frac{- 21.7 \times 1 0 ^{- 19}}{n ^{2}} J$
Calculate the longest wavelength of electron from the third Bohr's orbit of the $H e^{+}$ ion.