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  • The radius of the orbit of an electron in hydrogen-like atom (atomic number Z ) is where <img alt="\mathrm{a}_0" src

The radius of the orbit of an electron in hydrogen-like atom (atomic number Z ) is 4.5 \mathrm{a}_0 where \mathrm{a}_0 is the Bohr radius. Its orbital angular momentum is \mathrm{\frac{3 h}{2 \pi}}. The value of Z is:

Option: 1

2


Option: 2

3


Option: 3

4


Option: 4

5


Answers (1)

best_answer

According to Bohr’s quantisation condition \mathrm{\mathrm{L}=\frac{\mathrm{nh}}{2 \pi}}

Given: \mathrm{L}=\frac{3 \mathrm{~h}}{2 \pi} \quad \quad\therefore \frac{3 \mathrm{~h}}{2 \pi}=\frac{\mathrm{nh}}{2 \pi}\quad\quad\quad\quad \quad \text { or } \quad \mathrm{n}=3

Radius of nth orbit for hydrogen-like atom is \mathrm{\mathrm{r}_{\mathrm{n}}=\frac{\mathrm{n}^2}{\mathrm{Z}} \mathrm{a}_0}

Where \mathrm{a}_0 is the Bohr radius

Here, \mathrm{\mathrm{r}_{\mathrm{n}}=4.5 \mathrm{a}_0}

\mathrm{\therefore \quad 4.5 \mathrm{a}_0=\frac{(3)^2}{\mathrm{Z}} \mathrm{a}_0 \quad \text { or } \quad \mathrm{Z}=\frac{9}{4.5}=2}

Posted by

seema garhwal

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