The ratio of areas within the electron orbits for the first excited state to the ground state for hydrogen atom, is

Question

The ratio of areas within the electron orbits for the first excited state to the ground state for hydrogen atom, is (A)  16:1  (B)  18:1  (C)  4:1  (D)  2:1

Tardigrade Admin · Accepted Answer

Radius of orbit rn propto n2 For first excited state n=2 and for ground state, n=1 ∴ (r2/r1)=((2/1))2=(4/1) ∴ Ratio of areas =((r2/r1))2 =((4/1))2=16: 1

Q. The ratio of areas within the electron orbits for the first excited state to the ground state for hydrogen atom, is

$16 : 1$

$18 : 1$

$4 : 1$

$2 : 1$

Radius of orbit $r_{n} \propto n^{2}$
For first excited state $n = 2$
and for ground state, $n = 1$
$∴ \frac{r _{2}}{r _{1}} = (\frac{2}{1})^{2} = \frac{4}{1}$
$∴$ Ratio of areas $= (\frac{r _{2}}{r _{1}})^{2}$
$= (\frac{4}{1})^{2} = 16 : 1$

Q. The ratio of areas within the electron orbits for the first excited state to the ground state for hydrogen atom, is

16:1

18:1

4:1

2:1

Radius of orbit rn​∝n2 For first excited state n=2 and for ground state, n=1 ∴r1​r2​​=(12​)2=14​ ∴ Ratio of areas =(r1​r2​​)2 =(14​)2=16:1

$16 : 1$

$18 : 1$

$4 : 1$

$2 : 1$

Radius of orbit $r_{n} \propto n^{2}$
For first excited state $n = 2$
and for ground state, $n = 1$
$∴ \frac{r _{2}}{r _{1}} = (\frac{2}{1})^{2} = \frac{4}{1}$
$∴$ Ratio of areas $= (\frac{r _{2}}{r _{1}})^{2}$
$= (\frac{4}{1})^{2} = 16 : 1$