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Question

Physics Question on Atoms

If an electron is revolving around the hydrogen nucleus at a distance of 0.1 nm0.1 \,nm , what should be its speed ?

A

2.188×106 ms−12.188 \times 10^6 \,ms^{-1}

B

1.094×106 ms−11.094 \times 10^6 \,ms^{-1}

C

4.376×106 ms−14.376 \times 10^6 \,ms^{-1}

D

1.59×106 ms−11.59 \times 10^6 \,ms^{-1}

Answer

1.59×106 ms−11.59 \times 10^6 \,ms^{-1}

Explanation

Solution

Electrostatic force == centripetal force
14πε0Ze2r2\frac{1}{4 \pi \varepsilon_{0}} \frac{Z e^{2}}{r^{2}}
=mv2r=\frac{m v^{2}}{r}
∴v=(14πε0Ze2mr)\therefore v=\sqrt{\left(\frac{1}{4 \pi \varepsilon_{0}} \frac{Z e^{2}}{m r}\right)}
=9×109×1×(1.6×10−19)2(9.1×10−31)×(0.1×10−9)=\sqrt{\frac{9 \times 10^{9} \times 1 \times\left(1.6 \times 10^{-19}\right)^{2}}{\left(9.1 \times 10^{-31}\right) \times\left(0.1 \times 10^{-9}\right)}}
=1.59×106ms−1=1.59 \times 10^{6} ms ^{-1}