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Q.

A hydrogen atom, initially in the ground state, is excited by absorbing a photon of wavelength $980 Å$ . What will be the radius of the atom in the excited state, in terms of Bohr radius $a_{0}$ ? $(h c = 12500 eV - Å)$

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a

$16 a_{0}$

b

$4 a_{0}$

c

$9 a_{0}$

d

$25 a_{0}$

answer is B.

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Detailed Solution

energy of photon, $E_{photon} = \frac{12500}{980} ≃ 12.75 eV$

Final energy state, $E_{f} = E_{i} + E_{photon} = - 13.6 + 12.75 = - 0.85 eV$

$\Rightarrow E_{f} = \frac{- 13.6}{n^{2}} = - 0.85$

$\Rightarrow n = \sqrt{\frac{- 13.6}{- 0.85}} = 4$

$\Rightarrow r_{f} = r_{i} (n^{2}) = 16 a_{0}$

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A hydrogen atom, initially in the ground state, is excited by absorbing a photon of wavelength 980 Å. What will be the radius of the atom in the excited state, in terms of Bohr radius a0? (hc=12500 eV-Å)