What is the ratio of radii of the orbits corresponding to first excited state and ground state, in a hydrogen atom?

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In the Bohr model of the hydrogen atom, the radii of the electron orbits are given by the formula: rn=n2⋅h24π2⋅m⋅k⋅e2rn=4π2⋅m⋅k⋅e2n2⋅h2 where: rnrn is the radius of the orbit corresponding to the nn-th energy level, nn is the principal quantum number...
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In the Bohr model of the hydrogen atom, the radii of the electron orbits are given by the formula: rn=n2⋅h24π2⋅m⋅k⋅e2rn=4π2⋅m⋅k⋅e2n2⋅h2 where: rnrn is the radius of the orbit corresponding to the nn-th energy level, nn is the principal quantum number of the orbit, hh is the Planck constant (6.62607015×10−346.62607015×10−34 m² kg / s), mm is the mass of the electron (9.10938356×10−319.10938356×10−31 kg), kk is the Coulomb's constant (8.9875517923×1098.9875517923×109 N m² / C²), ee is the elementary charge (1.602176634×10−191.602176634×10−19 C). The ratio of the radii of two orbits corresponding to different energy levels n1n1 and n2n2 can be expressed as: rn2rn1=n12n22rn1rn2=n22n12 For the first excited state (n2=2n2=2) and the ground state (n1=1n1=1) of the hydrogen atom, the ratio of radii is: r2r1=1222=14r1r2=2212=41 Therefore, the ratio of the radii of the orbits corresponding to the first excited state and the ground state in a hydrogen atom is 1441. read less
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