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

Options

A. `2.188xx10^(6) ms^(-1)`
B. `1.094xx10^(6) ms^(-1)`
C. `4.376xx10^(6) ms^(-1)`
D. `1.60xx10^(6) ms^(-1)`

Answer

D

Explanation

Given, radius r=0.1 nm
We know, that `r_(n)=(n^(2))/(Z)r_(0)`
For `n=1,r_(0)=0.53Å=0.53xx10^(-10)m`
`" " 5.3xx10^(-11)=5.3xx10^(-2)xx10^(-9)=0.053nm`
Accroding to the question,
`" " r_(n)=0.1 nm =(n^(2))/(1)xx0.053nm`
`rArr " " n^(2)=(0.1)/(0.053)=(100)/(53) rArrn=(10)/(sqrt(53))`
We know We known that `mvr=(nh)/(2pi)rArrv=(nh)/(2pimr)`
By putting the vlaues above gives, `v=1.60xx10^(6)` m/s