The following energy states are shown for a atom such as hydrogen. The radius of first orbit of Bohr is ......

Options

A. `0.265Å`
B. `0.53Å`
C. `0.132Å`
D. none of these

Answer

A

Explanation

`E_(n)=-(13.6Z^(2))/(n^(2))eV` and `r_(n)=0.53(n^(2))/(Z)Å`
Here for H, n=1 and `E_(1)=-54.4eV`
`:.-54.4=-(13.6Z^(2))/(1^(2))`
`:.(54.4)/(13.6)=Z^(2)`
`:.4=Z^(2)`
`:.Z=2`
Radius of Bohr orbit `r_(1)=(0.53(1)^(2))/(2)[:.n=1]`
`=(0.53)/(2)=0.265Å`