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Question

Physics Question on Atoms

If 13.6 eV13.6 \,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

5.3×10−11m5.3 \times10^{-11} m

B

4.3×10−11m4.3 \times10^{-11} m

C

6.3×10−11m6.3 \times10^{-11} m

D

7.3×10−11m7.3 \times10^{-11} m

Answer

5.3×10−11m5.3 \times10^{-11} m

Explanation

Solution

Here, E=−13.6 eVE = -13.6\, eV =−13.6×1.6×10−19= -13.6 \times1.6 \times10^{-19} =−2.2×10−18J= -2.2 \times10^{-18} J E=−e28πε0r E = \frac{-e^{2}}{8\pi \varepsilon_{0}r} ∴ \therefore As orbital radius, r=−e28πε0E r= \frac{-e^{2}}{8\pi \varepsilon_{0}E} =9×109×(1.6×10−19)22×(2.2×10−18)= \frac{9\times10^{9} \times\left(1.6\times10^{-19}\right)^{2}}{2\times\left(2.2\times10^{-18}\right)} =5.3×10−11m= 5.3 \times10^{-11} m.