In which of the following systems will the radius of the first orbit (n=1) be minimum?

  • Option 1)

    Hydrogen atom

  • Option 2)

    Doubly ionized lithium

  • Option 3)

    Singly ionized helium

  • Option 4)

    Deuterium atom

 

Answers (1)

As we learnt in 

Radius of nth orbital -

r_{n}= frac{epsilon _{0}n^{2}h^{2}}{pi mZe^{2}}

 

- wherein

r_{n}alpha : frac{n^{2}}{Z}

frac{epsilon_{0}h^{2}}{pi me^{2}}= 0.529A^{circ}

 

 

\\ r=r_{o}*\frac{n^{2}}{Z} \: \: \: \: \: \: =\frac{r_{o}}{Z} (\because n=1) \\ \\ \therefore r\propto \frac{1}{Z}

r will be minimum for doubly ionized lithium since it has highest value of Z=3


Option 1)

Hydrogen atom

Incorrect

Option 2)

Doubly ionized lithium

Correct

Option 3)

Singly ionized helium

Incorrect

Option 4)

Deuterium atom

Incorrect

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