Modern Physics 1 Question 12

9. 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 a0 will be (Take hc=12500eV\AA)

(Main 2019, 11 Jan I)

(a) 4a0

(b) 9a0

(c) 16a0

(d) 25a0

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Solution:

  1. We know that net change in energy of a photon in a transition with wavelength λ is ΔE=hc/λ.

Here, hc=12500eV\AA and λ=980\AA

ΔE=12500/980=12.76eVEnE1=12.76eV

Since, the energy associated with an electron in nth  Bohr’s orbit is given as,

En=13.6n2eVEn=E1+12.76eV=13.6(1)2+12.76=0.84

Putting this value in Eq. (i)

n2=13.60.84=16n=4

and radius of nth  orbit, rn=n2a0rn=16a0



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