Question
When hydrogen atom is in its first excited level, its radius is
A.
four times, its ground state radius
B.
twice, its ground state radius
C.
same as its ground sate radius
D.
half of its ground state radius
Answer :
four times, its ground state radius
Solution :
The radius of $$n$$th Bohr's orbit of hydrogen and hydrogen like atom
$$\eqalign{
& {r_n} = \frac{{{\varepsilon _0}{n^2}{h^2}}}{{\pi m{e^2}Z}} \cr
& \therefore {r_n} = \frac{{{n^2}{a_0}}}{Z}\,\,{\text{or}}\,\,{r_n} \propto \frac{{{n^2}}}{Z} \cr} $$
For ground state, $$n =1$$
Atomic number, $$Z = 1$$
For first excited state, $$n = 2$$
$$\therefore \frac{{{r_2}}}{{{r_1}}} = {\left( {\frac{2}{1}} \right)^2} = 4\,\,{\text{or}}\,\,{r_2} = 4{r_1}$$
Therefore, radius of first excited state is 4 times than that of ground state radius in $$H$$-atom.