If 13.6 eV energy is required to separate a hydrogen atom into a proton and an electron, then the orbital radius of electron in a hydrogen atom is

Question

If 13.6 eV energy is required to separate a hydrogen atom into a proton and an electron, then the orbital radius of electron in a hydrogen atom is (A) 5.3 ×10-11 m (B) 4.3 ×10-11 m (C) 6.3 ×10-11 m (D) 7.3 ×10-11 m

Tardigrade Admin · Accepted Answer

Here, E = -13.6 eV = -13.6 ×1.6 ×10-19 = -2.2 ×10-18 J E = (-e2/8π ε0r) ∴ As orbital radius, r= (-e2/8π ε0E) = (9×109 ×(1.6×10-19)2/2×(2.2×10-18)) = 5.3 ×10-11 m.

Q. If $13.6 e V$ energy is required to separate a hydrogen atom into a proton and an electron, then the orbital radius of electron in a hydrogen atom is

$5.3 \times 1 0^{- 11} m$

$4.3 \times 1 0^{- 11} m$

$6.3 \times 1 0^{- 11} m$

$7.3 \times 1 0^{- 11} m$

Q. If 13.6eV energy is required to separate a hydrogen atom into a proton and an electron, then the orbital radius of electron in a hydrogen atom is

5.3×10−11m

4.3×10−11m

6.3×10−11m

7.3×10−11m

Here, E=−13.6eV =−13.6×1.6×10−19 =−2.2×10−18J E=8πε0​r−e2​ ∴ As orbital radius, r=8πε0​E−e2​ =2×(2.2×10−18)9×109×(1.6×10−19)2​ =5.3×10−11m.

Q. If $13.6 e V$ energy is required to separate a hydrogen atom into a proton and an electron, then the orbital radius of electron in a hydrogen atom is

$5.3 \times 1 0^{- 11} m$

$4.3 \times 1 0^{- 11} m$

$6.3 \times 1 0^{- 11} m$

$7.3 \times 1 0^{- 11} m$