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In hydrogen and hydrogen like atoms the ...

In hydrogen and hydrogen like atoms the ratio of difference of energy `E_(4n)-E_(2n)` and `E_(2n)-E_(n)` varies with atomic number Z and principal quantum number n as

A

`z^(2)//n^(2)`

B

`z^(4)//n^(4)`

C

`z//n`

D

`(n^(2)//z^(2))`

Text Solution

Verified by Experts

The correct Answer is:
D
`E_(n)= -13.6/n^(2) (Z^(2))`
`E_(2n)= -13.6/((2n)^(2)) Z^(2)=13.6/4 (Z^(2)/n^(2))`
`E_(2n)-E_(n)=[(-13.6/4)Z^(2)/n^(2)]-[-3.6 (Z^(2)/n^(2))]`
`E_(2n)-E_(n)= -(13.6 )/(4) Z^(2)/n^(2)+13.6 Z^(2)/n^(2)`
`E_(2n)-E_(n)=Z^(2)/n^(2) (13.6-13.6/4)=(10.2) (Z^(2)/n^(2))`
`(E_(2n))(E_(n))=((13.6)^(2))/(4) (Z^(4)/n^(4))`
`((E_(2n)-E_(n)))/((E_(2n))(E_(n)))=((10.2)(Z^(2)/n^(2)))/(((13.6)^(2))/4 (Z^(4)/n^(4))) implies ((E_(2n)-E_(n)))/((E_(2n))(E_(n))) prop (n^(2)/Z^(2))`
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