Give the correct order of initials T (true) or F (false) for following statements.(i) The ratio of the radii of the first three Bohr orbit of hydrogen atom is 1 : 8 : 27 (ii) The ratio of magnitude of Total Energy : Kinetic Energy : Potential Energy for any orbit is 1 : 1 : 2 (iii) The frequency of a green light is 6 × 1014 Hz, then its wavelength is 500 nm (iv) The ratio of de-broglie wavelength of a 'H' atom, 'He' atom and CH4 molecule moving with equal kinetic energy is 4 : 2 : 1

Engineering

Chemistry

Bohrs Model for Hydrogen Atom

Dual Behaviour and de Broglie Hypothesis

Question

Give the correct order of initials T (true) or F (false) for following statements.
(i) The ratio of the radii of the first three Bohr orbit of hydrogen atom is 1 : 8 : 27
(ii) The ratio of magnitude of Total Energy : Kinetic Energy : Potential Energy for any orbit is   1 : 1 : 2
(iii) The frequency of a green light is 6 × 10¹⁴ Hz, then its wavelength is 500 nm
(iv) The ratio of de-broglie wavelength of a 'H' atom, 'He' atom and CH₄ molecule moving with equal kinetic energy is 4 : 2 : 1

FTFT

FTTT

FFTT

TFTF

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(i) $rα \frac{n^{2}}{Z}$ , r₁ : r₂ : r₃ ⇒ 1 : 4 : 9    $∴$ False
(ii)   | P.E.| = $\frac{{Ze}^{2}}{r}$ , |K.E.| = $\frac{{Ze}^{2}}{2 r}$
       & |T.E.| = $\frac{{Ze}^{2}}{2 r}$ $∴$ True
(iii) $λ = \frac{C}{ν} = \frac{3 \times 10^{8}}{6 \times 10^{14}}$ = 0.5 × 10⁶ m
      = 500 × 10^–9 m
       = 500 mm $∴$ True
(iv) $λ = \frac{h}{\sqrt{2 (K . E .) m}}$
$λ_{H} : λ_{He} : λ_{{CH}_{4} =} \frac{1}{\sqrt{1}} : \frac{1}{\sqrt{4}} : \frac{1}{\sqrt{16}}$

$= \frac{1}{1} : \frac{1}{2} : \frac{1}{4} \Rightarrow$ 4 : 2 : 1 $∴$ True