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Calculate the velocity of an electron pl...

Calculate the velocity of an electron placed in the `3^("rd")` orbit of `He^(2+)` ion.

Text Solution

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Velocity of electron `=(2.18xx10^(6)xx Z)/(n) ms^(-1)= (2.18xx10^(6)xx2)/(3)=1.453xx10^(6)ms^(-1)`
Radius of the 3rd orbit of `He^(2+)=(r_(1)(n)^(2))/(Z)=(0.529xx3^(2))/(2)=(0.529xx9)/(2)=2.3805Å=2.3805xx10^(-10)m`
Number of revolutions/sec `=(1)/(2pi r//v)=(v)/(2pi r)=(1.453xx10^(6)ms^(-1))/(2.3805xx10^(-10)m)=6.104xx10^(15)s^(-1)`
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