Let T 1 and T 2 be the energy of an electron in the first and second excited states of hydrogen atom, respectively. According to the Bohr's model of an atom, the ratio T 1: T 2 is :

Question

Let T 1 and T 2 be the energy of an electron in the first and second excited states of hydrogen atom, respectively. According to the Bohr's model of an atom, the ratio T 1: T 2 is : (A) 9: 4 (B) 1: 4 (C) 4: 1 (D) 4: 9

Tardigrade Admin · Accepted Answer

First excited state ⇒ n =2 T 1=-13.6 ( z 2/ n 2)=-(13.6/4) eV Second excited state ⇒ n =3 T 2=-13.6 ( z 2/ n 2)=-(13.6/9) eV T 1: T 2=(1/4): (1/9)=9: 4

Q. Let $T_{1}$ and $T_{2}$ be the energy of an electron in the first and second excited states of hydrogen atom, respectively. According to the Bohr's model of an atom, the ratio $T_{1} : T_{2}$ is :

$9 : 4$

$1 : 4$

$4 : 1$

$4 : 9$

First excited state $\Rightarrow n = 2$
$T_{1} = - 13.6 \frac{z ^{2}}{n ^{2}} = - \frac{13.6}{4} e V$
Second excited state $\Rightarrow n = 3$
$T_{2} = - 13.6 \frac{z ^{2}}{n ^{2}} = - \frac{13.6}{9} e V$
$T_{1} : T_{2} = \frac{1}{4} : \frac{1}{9} = 9 : 4$

Q. Let T1​ and T2​ be the energy of an electron in the first and second excited states of hydrogen atom, respectively. According to the Bohr's model of an atom, the ratio T1​:T2​ is :

9:4

1:4

4:1

4:9