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The radius of the first orbit of hydroge...

The radius of the first orbit of hydrogen atom is 0.5 Å. The electron moves is an orbit with a uniform speed of 2.2`xx10^(6) ms^(-1)`. What is the magnetic field produced at the centre of the uncleus due to the mation of this electron ? Use `mu_(0) = 4pi xx 10^(-7) Hm^(-1)` and electric charge ` =1.6 xx 10^(-19)` C

Text Solution

Verified by Experts

Here, `" " r = 0.5 Å xx 10^(-10) `m
v = 2.2 `xx 10^(6) ms^(-1)`
period of revolution of electron
T = `(2pi r)/(v) = (2 xx 22 xx 0.5 xx 10^(-10))/(7 xx 2.2 xx 10^(6)) = (1)/(7) xx 10^(-15)`S
Equivalent current, I = `("charge")/("time") = (e)/(T) = (1.6xx 10^(-19) xx 7)/(10^(-15)) `
Magnetic field produced at the centre of the nucleus,
`B = (mu_(0)I)/(2r) = (4pi xx 10^(-7) xx 1.12 xx 10^(-3))/(2 xx 0.5xx 10^(-10))`
B = 14.07 T
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