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The energy of a hydrogen atom in a giv...

The energy of a hydrogen atom in a given orbit is -3.4 eV . Find the radius of the orbit .
`["given" ,e =-1.610^(-19)C, m_e=9.1110^(-31) kg,h/(2pi)=1.055xx10^(-34)J*s,1/(4piin_0)=9xx10^(9)N*m^2C^(-2)]`

Text Solution

Verified by Experts

We know ,`E_n prop 1/(n^2)`
`therefore (E_1)/(E_2)=(n_2^2)/(n_1^2) or, (-13.6)/(-3.4)=(n_2^2)/1 or, n_2=2`
`"Again" ,r_n=(in_0n^2h^2)/(pime^2)`
`or, r_2=(8.85xx10^(-12)xx4xx(6.63xx10^(-34))^2)/(pixx9.11xx10^(-34)xx(1.6xx10^(-19))^2)`
`=(1.5xx10^(-77))/(7.33xx10^(-68))=2.13xx10^(-10)m=2.13 "Å"`
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