A hydrogen atom, initially in the ground state is excited by absorbing a photon of wavelength $980 \AA$. The radius of the atom in the excited state, in terms of Bohr radius $a_{0}$, will be: ($hc=12500 \mathrm{eV}$ - Å)

JEE Main · 2019 · 11 Jan 2019 · Shift 1 · Modern Physics

A hydrogen atom, initially in the ground state is excited by absorbing a photon of wavelength

980 \overset{˚}{A}

. The radius of the atom in the excited state, in terms of Bohr radius

a_{0}

, will be:
(

h c = 12500 eV

- Å)

(A) $25 a_{0}$
(B) $9 a_{0}$
(C) $16 a_{0}$ ✓ Correct
(D) $4 a_{0}$

Answer: (C)

Solution

The absorbed photon carries energy

E = \frac{h c}{λ} = \frac{12500}{980} \approx 12.75 eV

. Lifting the atom from the ground state to level

n

needs

13.6 (1 - \frac{1}{n ^{2}})

eV, so setting

13.6 (1 - \frac{1}{n ^{2}}) = 12.75

gives

1 - \frac{1}{n ^{2}} \approx 0.938

, hence

n^{2} \approx 16

and

n = 4

. Since the Bohr radius grows as

r = n^{2} a_{0}

, the excited atom has radius

16 a_{0}

JEE Main · 2019 · 11 Jan 2019 · Shift 1 · Single correct option

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